I do not understand the solution to this problem. Please help!

The Problem:

"The integer A consists of 666 threes, and the integer B has 666 sixes. What digits appear in the product AB?"

The (partial) Solution:

"Since 6 = 3 x 2, the product in question will be the same as that obtained by multiplying the integer A1 composed of 666 digits 9 by the integer B1 composed of 666 digits 2. etc."

Does anyone understand what this means? This is problem #72 from the USSR Olympiad Problem Book.