回复：I'm 10 year old kid. Please use very simple working.

Sorry. I can't come here during daytime. The idea behind the generating function is like this:

Every x^92 you get from the product is corresponding to a feasible combination: for example, x^92=(x^1)^2*(x^10)^4*x^50 is corresponding to a combination of 2 pennies, 4 dimes, and 1 half dollar, whose sum is 92 cents.

To view this method another way, suppose there are 5 pennies and one nickel(five cents). (1+x+x^2+x^3+x^4+x^5)(1+x^5)= 1+x+x^2+x^3+x^4+2x^5+x^6+...+x^10.
There are two ways to get five cents, as the coefficient of x^5 is 2.