Answer
$$y=-\frac{2\ln3}{\ln12}$$
Work Step by Step
$$4^{-y}=3^{y+2}$$
Take the natural logarithm of both sides:
$$\ln(4^{-y})=\ln(3^{y+2})$$
Remember that $\ln x^a=a\ln x$
$$-y\ln4=(y+2)\ln3$$ $$-y\ln4=y\ln3+2\ln3$$ $$y\ln3+y\ln4=-2\ln3$$ $$y(\ln3+\ln4)=-2\ln3$$
Also, $\ln x+\ln y=\ln(xy)$
$$y\ln12=-2\ln3$$ $$y=-\frac{2\ln3}{\ln12}$$
