Answer
$x=-\dfrac{16}{9}$
Work Step by Step
The given expression can be re-arranged as:
$8^{6+3x}=(2^3)^{6+3x} \\ =2^{18+9x}$
Thus, the term $2^{18+9x}$ is equivalent to:
$2^{18+9x}=2^2$
The base is the same, so both sides can be equal when the exponents are equal.
Therefore, we simplify as follows:
$18+9x =2\\
9x=2-18\\
9x=-16\\
\dfrac{9x}{9}=\dfrac{-16}{9}\\
x=-\dfrac{16}{9}$
