Explanation:

When we say "I could work hard when I was young," it means that the person had the ability or the capacity to work hard during their youth. In this context, the word "could" is used to express past ability or past possibility. Let's break down the options to understand why option 'D' is the correct answer.

a) May:
- "I may work hard when I was young" implies that there was a possibility of working hard when the person was young, but it does not convey the idea that they actually did work hard. It suggests uncertainty rather than a definite action.

b) Can:
- "I can work hard when I was young" is incorrect because "can" is used to express present ability or possibility. It does not fit in the past tense context of the sentence.

c) Must:
- "I must work hard when I was young" implies that there was an obligation or necessity to work hard when the person was young. However, it does not convey the idea that they actually did work hard. It suggests a requirement rather than a past action.

d) Could:
- "I could work hard when I was young" is the correct option. It indicates that the person had the ability or capacity to work hard during their youth. It suggests that they actually did work hard.

Therefore, the correct answer is option 'D' - "I could work hard when I was young." It accurately conveys the past ability or possibility of working hard during the person's youth.