[tex]\it \Big A_x^4\cdot\Big P_{x-4}=42\cdot\Big P_{x-2} \Rightarrow \dfrac{x!}{(x-4)!}\cdot (x-4)!=42\cdot(x-2)! \Rightarrow \\ \\ \\ \Rightarrow x!=42\cdot(x-2)! \Rightarrow (x-2)!\cdot(x-1)\cdot x =42\cdot(x-2)!\ \Big |_{:(x-2)!} \Rightarrow \\ \\ \\ \Rightarrow (x-1) \cdot x=42=6\cdot7 \Rightarrow x=7[/tex]
