MySQL 8.0

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WITH Payment AS (
    SELECT 1 AS id, 250 AS cust_id, 1 AS mnth, 2 AS year, 1200 AS amount UNION ALL
    SELECT 2, 300, 1,  2, 2400 UNION ALL
    SELECT 3, 450, 12, 3, 1200 UNION ALL
    SELECT 4, 450, 1,  4, 1200 UNION ALL
    SELECT 5, 300, 3,  2, 1200 UNION ALL
    SELECT 6, 455, 1,  3, 1200
)

SELECT
    p1.id,
    p1.cust_id,
    p1.mnth,
    p1.year,
    p1.amount
FROM
(
    SELECT id, cust_id, mnth, year, amount,
        CASE WHEN CONCAT('%,', mnth, ',%') LIKE '%,12,%' THEN 12
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,11,%' THEN 11
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,10,%' THEN 10
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,9,%' THEN 9
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,8,%' THEN 8
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,7,%' THEN 7
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,6,%' THEN 6
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,5,%' THEN 5
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,4,%' THEN 4
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,3,%' THEN 3
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,2,%' THEN 2
             WHEN CONCAT('%,', mnth, ',%') LIKE '%,1,%' THEN 1 END AS mnth_num
    FROM Payment
) p1
INNER JOIN
(
    SELECT
        MAX(CASE WHEN CONCAT('%,', mnth, ',%') LIKE '%,12,%' THEN 12
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,11,%' THEN 11
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,10,%' THEN 10
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,9,%' THEN 9
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,8,%' THEN 8
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,7,%' THEN 7
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,6,%' THEN 6
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,5,%' THEN 5
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,4,%' THEN 4
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,3,%' THEN 3
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,2,%' THEN 2
                 WHEN CONCAT('%,', mnth, ',%') LIKE '%,1,%' THEN 1 END) AS max_mnth,
        MAX(year) AS max_year
    FROM Payment
    WHERE year = (SELECT MAX(year) FROM Payment)
) p2
    ON p1.year = p2.max_year AND
       p1.mnth_num = p2.max_mnth;

id	cust_id	mnth	year	amount
4	450	1	4	1200