Find the coefficient of $x^6$

Question

I can not understand how to solve it .

Can anybody provide me a hint .

Added: There solution is also given but I could not understand it .

Answer 1

HINT

Multipliers over 6 does not change coefficient of $x^6$

Answer 2

Try multiplying out some terms and ignoring those where the exponent is too big. For example you could start with

$(1+x)(1+2x^2+x^4)(1+3x^3+3x^6+\cdots)(1+4x^4+\cdots)(1+5x^5+\cdots)(1+6x^6+\cdots)$