[tex]\it a)\ \ 3n!=360\bigg|_{:3} \Rightarrow n!=120=5! \Rightarrow n=5\\ \\ \\ b)\ \ 6(n-1)!=(n+1)! \Rightarrow 6(n-1)!=(n-1)!\cdot n(n+1)\bigg|_{:(n-1)!} \Rightarrow \\ \\ \\ \Rightarrow 6=n(n+1) \Rightarrow n(n+1)=6=2\cdot3 \Rightarrow n=2[/tex]
[tex]\it c)\ \ (n+4)!-n(n+3)!=96 \Rightarrow (n+3)!(n+4-n)=96 \Rightarrow \\ \\ \\ \Rightarrow (n+3)!\cdot4=96\bigg|_{:4} \Rightarrow (n+3)!=24=4! \Rightarrow n+3=4 \Rightarrow n=1[/tex]
