Hello from MrBillDoesMath!
Answer:
Suppose "a" is even. Then "a" is a multiple of the number 2, say a = 2k (where k is an integer), Then the product
ab = (2k)b = 2(kb)
is also a multiple of 2 and therefore even. In other words, the statement in the Question is true.
Thank you,
MrB