Binomial theorem:
\((x-y)^n=\displaystyle\sum_{k=0}^n\binom nkx^k(-y)^{n-k}\)
The term with \(x^4y^{18}\) corresponds to \(n=18+4=22\) and \(k=4\) (or \(k=18\), since \(\dbinom nk=\dbinom n{n-k}\)).
So, the coefficient of this term is
\(\dbinom{22}4(-1)^{18}=\dbinom{22}4=\dfrac{22!}{4!(22-4)!}=7315\)
