This is Velleman's exercise 3.4.26 (b):
Prove that it is NOT true that for every integer $n$, 60 divides $n$ iff 6 divides $n$ and 10 divides $n$.
I do understand that a number will be divisible by 6 and 10 if it is divisible by 60 and that it will not necessarily be divisible by 60 if it is divisible by 6 and by 10. 30 is an example of it.
I still have an issue actually discovering and writing up the proof. To illustrate the issue and to put the question in context, I would like to refer to the first part of the question already asked by another user, Velleman's exercise 3.4.26 (a). Thanks in advance.