Answer
$$x = \left\{ {1,2} \right\}$$
Work Step by Step
$$\eqalign{
& {4^x} - 6\left( {{2^x}} \right) = - 8 \cr
& {\text{Write }}{{\text{4}}^x}{\text{ as }}{\left( {{2^2}} \right)^x} \cr
& {\left( {{2^2}} \right)^x} - 6\left( {{2^x}} \right) = - 8 \cr
& or \cr
& {\left( {{2^x}} \right)^2} - 6\left( {{2^x}} \right) = - 8 \cr
& {\text{Add 8 to both sides}} \cr
& {\left( {{2^x}} \right)^2} - 6\left( {{2^x}} \right) + 8 = 0 \cr
& {\text{Factoring}} \cr
& \left( {{2^x} - 4} \right)\left( {{2^x} - 2} \right) = 0 \cr
& {\text{Zero - product property}} \cr
& {2^x} - 4 = 0{\text{ or }}{2^x} - 2 = 0 \cr
& {2^x} = 4{\text{ or }}{2^x} = 2 \cr
& x = 2,\,\,\,\,\,\,\,\,\,\,{\text{or}}\,\,\,\,\,\,\,\,\,\,\,\,\,x = 1 \cr
& \cr
& {\text{The solution set is }}x = \left\{ {1,2} \right\} \cr} $$
