jmc

Since $8={\left(\frac{1}{2}\right)}^{-3}$ the equation can be rewritten as ${\left(\frac{1}{2}\right)}^{-3(4x-6)}={\left(\frac{1}{2}\right)}^{x+5}$. From this equation, we see that $-3(4x-6)=x+5$. Simplifying we get, $$\begin{array}{rl}-12x+18& =x+5\\ \Rightarrow -13x+18& =5\\ \Rightarrow -13x& =-13\\ \Rightarrow x& =\boxed{1}.\end{array}$$