\((a+b)^n=\displaystyle\sum_{k=0}^n\binom nka^{n-k}b^k\)
where \(\dbinom nk=\dfrac{n!}{k!(n-k)!}\). The second term of the expansion occurs when \(k=1\).
So the second term of the expansion of \((2r-3s)^{12}\) is
\(\dbinom{12}1(2r)^{12-1}(-3s)^1=12(2r)^{11}(-3s)=-73728r^{11}s\)
