Sunil is 38 today and his nephew is 14. How many years ago was Sunil's age three times his nephew's age?

Going back $t$ years, $38-t=3(14-t)$, that is $38-t=42-3t$, so $2t=4$ and $t=2$. Check: two years ago they were 36 and 12, and $36=3\times 12$. 4 is the intermediate value $2t$, taken before the final halving. 12 is the nephew's age at that moment - the right year, the wrong quantity. 24 is the gap between their ages, which never changes and so can never be the answer to a 'how many years ago' question here.