A number leaves remainder 19 when divided by 36. The remainder when the same number is divided by 12 is:

Write the number as 36k + 19. Since 36 is a multiple of 12, the term 36k contributes nothing to the remainder, so only 19 matters: 19 = 12 + 7. The remainder is therefore 7. (A remainder of 19 is impossible for a divisor of 12 — it must be smaller than the divisor.)