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$8^{4x+2}=64$
$8^{4x+2}=8^2$
Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. $\begin{gathered} 8^{{\color{#0000FF}{4x+2}}}=8^{{\color{#0000FF}{2}}} \quad \Leftrightarrow \quad {\color{#0000FF}{4x+2}}={\color{#0000FF}{2}} \end{gathered}$ Finally, we will solve the equation $4x+2=2.$
$4x+2=2$
$4x=0$
$x=0$