Given the equation:
[tex]6^{2-3x}=6^{-2x-2}[/tex]
since both bases are 6, we can equate both exponents to get the following equation:
[tex]2-3x=-2x-2[/tex]
solving for x, we get:
[tex]\begin{gathered} 2-3x=-2x-2 \\ \Rightarrow-3x+2x=-2-2=-4 \\ \Rightarrow-x=-4 \\ \Rightarrow x=4 \end{gathered}[/tex]
therefore, the solution of the equation is x = 4
