MySQL 8.0

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WITH d AS (
    SELECT '2010-01' AS YearMonthDate UNION ALL
    SELECT '2010-02' UNION ALL
    SELECT '2010-03' UNION ALL
    SELECT '2010-04' UNION ALL
    SELECT '2010-05' UNION ALL
    SELECT '2010-06' UNION ALL
    SELECT '2010-07' UNION ALL
    SELECT '2010-08' UNION ALL
    SELECT '2010-08' UNION ALL
    SELECT '2010-09' UNION ALL
    SELECT '2010-10' UNION ALL
    SELECT '2010-11' UNION ALL
    SELECT '2010-12' UNION ALL
    SELECT '2011-01' UNION ALL
    SELECT '2011-02' UNION ALL
    SELECT '2011-03' UNION ALL
    SELECT '2011-04' UNION ALL
    SELECT '2011-05' UNION ALL
    SELECT '2011-06' UNION ALL
    SELECT '2011-07' UNION ALL
    SELECT '2011-08' UNION ALL
    SELECT '2011-08' UNION ALL
    SELECT '2011-09' UNION ALL
    SELECT '2011-10' UNION ALL
    SELECT '2011-11' UNION ALL
    SELECT '2011-12' UNION ALL
    SELECT '2012-01' UNION ALL
    SELECT '2012-02' UNION ALL
    SELECT '2012-03' UNION ALL
    SELECT '2012-04' UNION ALL
    SELECT '2012-05' UNION ALL
    SELECT '2012-06' UNION ALL
    SELECT '2012-07' UNION ALL
    SELECT '2012-08' UNION ALL
    SELECT '2012-08' UNION ALL
    SELECT '2012-09' UNION ALL
    SELECT '2012-10' UNION ALL
    SELECT '2012-11' UNION ALL
    SELECT '2012-12' UNION ALL
    SELECT '2013-01' UNION ALL
    SELECT '2013-02' UNION ALL
    SELECT '2013-03' UNION ALL
    SELECT '2013-04' UNION ALL
    SELECT '2013-05' UNION ALL
    SELECT '2013-06' UNION ALL
    SELECT '2013-07' UNION ALL
    SELECT '2013-08' UNION ALL
    SELECT '2013-08' UNION ALL
    SELECT '2013-09' UNION ALL
    SELECT '2013-10' UNION ALL
    SELECT '2013-11' UNION ALL
    SELECT '2013-12' UNION ALL
    SELECT '2014-01' UNION ALL
    SELECT '2014-02' UNION ALL
    SELECT '2014-03' UNION ALL
    SELECT '2014-04' UNION ALL
    SELECT '2014-05' UNION ALL
    SELECT '2014-06' UNION ALL
    SELECT '2014-07' UNION ALL
    SELECT '2014-08' UNION ALL
    SELECT '2014-08' UNION ALL
    SELECT '2014-09' UNION ALL
    SELECT '2014-10' UNION ALL
    SELECT '2014-11' UNION ALL
    SELECT '2014-12' UNION ALL
    SELECT '2015-01' UNION ALL
    SELECT '2015-02' UNION ALL
    SELECT '2015-03' UNION ALL
    SELECT '2015-04' UNION ALL
    SELECT '2015-05' UNION ALL
    SELECT '2015-06' UNION ALL
    SELECT '2015-07' UNION ALL
    SELECT '2015-08' UNION ALL
    SELECT '2015-08' UNION ALL
    SELECT '2015-09' UNION ALL
    SELECT '2015-10' UNION ALL
    SELECT '2015-11' UNION ALL
    SELECT '2015-12' UNION ALL
    SELECT '2016-01' UNION ALL
    SELECT '2016-02' UNION ALL
    SELECT '2016-03' UNION ALL
    SELECT '2016-04' UNION ALL
    SELECT '2016-05' UNION ALL
    SELECT '2016-06' UNION ALL
    SELECT '2016-07' UNION ALL
    SELECT '2016-08' UNION ALL
    SELECT '2016-08' UNION ALL
    SELECT '2016-09' UNION ALL
    SELECT '2016-10' UNION ALL
    SELECT '2016-11' UNION ALL
    SELECT '2016-12' UNION ALL
    SELECT '2017-01' UNION ALL
    SELECT '2017-02' UNION ALL
    SELECT '2017-03' UNION ALL
    SELECT '2017-04' UNION ALL
    SELECT '2017-05' UNION ALL
    SELECT '2017-06' UNION ALL
    SELECT '2017-07' UNION ALL
    SELECT '2017-08' UNION ALL
    SELECT '2017-08' UNION ALL
    SELECT '2017-09' UNION ALL
    SELECT '2017-10' UNION ALL
    SELECT '2017-11' UNION ALL
    SELECT '2017-12' UNION ALL
    SELECT '2018-01' UNION ALL
    SELECT '2018-02' UNION ALL
    SELECT '2018-03' UNION ALL
    SELECT '2018-04' UNION ALL
    SELECT '2018-05' UNION ALL
    SELECT '2018-06' UNION ALL
    SELECT '2018-07' UNION ALL
    SELECT '2018-08' UNION ALL
    SELECT '2018-08' UNION ALL
    SELECT '2018-09' UNION ALL
    SELECT '2018-10' UNION ALL
    SELECT '2018-11' UNION ALL
    SELECT '2018-12' UNION ALL
    SELECT '2019-01' UNION ALL
    SELECT '2019-02' UNION ALL
    SELECT '2019-03' UNION ALL
    SELECT '2019-04' UNION ALL
    SELECT '2019-05' UNION ALL
    SELECT '2019-06' UNION ALL
    SELECT '2019-07' UNION ALL
    SELECT '2019-08' UNION ALL
    SELECT '2019-08' UNION ALL
    SELECT '2019-09' UNION ALL
    SELECT '2019-10' UNION ALL
    SELECT '2019-11' UNION ALL
    SELECT '2019-12'
),
p AS
(
    SELECT 'Apple' AS ProductBrand UNION ALL
    SELECT 'Samsung' UNION ALL
    SELECT 'Sony' UNION ALL
    SELECT 'LG'
),
yourTable AS (
    SELECT 'Apple' AS ProductBrand, '2015-03' AS PurchasedDate, '2015-05' AS SoldDate UNION ALL
    SELECT 'Samsung', '2014-01', '2015-03' UNION ALL
    SELECT 'Sony',    '2016-02', '2016-05' UNION ALL 
    SELECT 'Sony',    '2013-01', '2013-08' UNION ALL
    SELECT 'Apple',   '2015-05', '2015-10' UNION ALL
    SELECT 'LG',      '2011-02', '2014-06' UNION ALL
    SELECT 'Samsung', '2017-02', '2017-04' UNION ALL
    SELECT 'LG',      '2016-01', '2016-06' UNION ALL
    SELECT 'LG',      '2018-06', '2019-01'
)

SELECT
    t.ProductBrand,
    d.YearMonthDate,
    COUNT(t.ProductBrand) AS NitemsInventory
FROM p
CROSS JOIN d
LEFT JOIN yourTable t
    ON d.YearMonthDate BETWEEN t.PurchasedDate AND t.SoldDate AND
       p.ProductBrand = t.ProductBrand
WHERE
    t.ProductBrand IS NOT NULL
GROUP BY
    t.ProductBrand,
    d.YearMonthDate;

ProductBrand	YearMonthDate	NitemsInventory
LG	2011-02	1
LG	2011-03	1
LG	2011-04	1
LG	2011-05	1
LG	2011-06	1
LG	2011-07	1
LG	2011-08	2
LG	2011-09	1
LG	2011-10	1
LG	2011-11	1
LG	2011-12	1
LG	2012-01	1
LG	2012-02	1
LG	2012-03	1
LG	2012-04	1
LG	2012-05	1
LG	2012-06	1
LG	2012-07	1
LG	2012-08	2
LG	2012-09	1
LG	2012-10	1
LG	2012-11	1
LG	2012-12	1
LG	2013-01	1
Sony	2013-01	1
LG	2013-02	1
Sony	2013-02	1
LG	2013-03	1
Sony	2013-03	1
LG	2013-04	1
Sony	2013-04	1
LG	2013-05	1
Sony	2013-05	1
LG	2013-06	1
Sony	2013-06	1
LG	2013-07	1
Sony	2013-07	1
LG	2013-08	2
Sony	2013-08	2
LG	2013-09	1
LG	2013-10	1
LG	2013-11	1
LG	2013-12	1
LG	2014-01	1
Samsung	2014-01	1
LG	2014-02	1
Samsung	2014-02	1
LG	2014-03	1
Samsung	2014-03	1
LG	2014-04	1
Samsung	2014-04	1
LG	2014-05	1
Samsung	2014-05	1
LG	2014-06	1
Samsung	2014-06	1
Samsung	2014-07	1
Samsung	2014-08	2
Samsung	2014-09	1
Samsung	2014-10	1
Samsung	2014-11	1
Samsung	2014-12	1
Samsung	2015-01	1
Samsung	2015-02	1
Samsung	2015-03	1
Apple	2015-03	1
Apple	2015-04	1
Apple	2015-05	2
Apple	2015-06	1
Apple	2015-07	1
Apple	2015-08	2
Apple	2015-09	1
Apple	2015-10	1
LG	2016-01	1
LG	2016-02	1
Sony	2016-02	1
LG	2016-03	1
Sony	2016-03	1
LG	2016-04	1
Sony	2016-04	1
LG	2016-05	1
Sony	2016-05	1
LG	2016-06	1
Samsung	2017-02	1
Samsung	2017-03	1
Samsung	2017-04	1
LG	2018-06	1
LG	2018-07	1
LG	2018-08	2
LG	2018-09	1
LG	2018-10	1
LG	2018-11	1
LG	2018-12	1
LG	2019-01	1