Answer:
[tex]\large\boxed{x=\dfrac{4}{3}}[/tex]
Step-by-step explanation:
[tex]4^{3x-6}=\dfrac{1}{16}\\\\4^{3x-6}=\dfrac{1}{4^2}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\4^{3x-6}=4^{-2}\iff3x-6=-2\qquad\text{add 6 to both sides}\\\\3x=4\qquad\text{divide both sides by 3}\\\\x=\dfrac{4}{3}[/tex]
