Finding the coefficient of $x^{18}$ in $({5x^6 + 3x^{-3}})^9$ Doing some homework and we were given the question below,

And a sample solution to a different question in roughly the same format:

I was just looking for some help in understanding the way to go about doing the question. My main issue is where did they determine that $x^2$ was equivalent to $x^{12}$. After that I should be good.
Thanks in advance

If you think about the binomial expansion, it consists of terms that are products of $x^6$ and $x^{-3}$  If you have $a$ terms of $x^6$ and $b$ terms of $x^{-3}$ you need $a+b=9, 6a-3b=18$. Solve those equations, then think about the binomial coefficient.
