Answer
$\frac{-16}{9}$
Work Step by Step
We know that $a^b=a^c\longrightarrow b=c$ if $a\ne1,a\ne-1$ (which applies here).
Hence here $8^{6+3x}=4\\(2^3)^{6+3x}=2^2\\2^{3(6+3x)}=2^2\\3(6+3x)=2\\18+9x=2\\9x=-16\\x=\frac{-16}{9}$
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