We can make the base of the equation same on both the sides and then equate the exponents to get the answer as shown below:
[tex] (\sqrt{6})^{8x}=(216)^{x-3} \\ \\
(\sqrt{6})^{8x}=(6^{3})^{x-3} \\ \\
(6^{\frac{1}{2}}) ^{8x}=(6)^{3x-9} \\ \\
(6)^{4x} =(6)^{3x-9} \\ \\
4x=3x-9\\ \\
4x-3x=-9\\ \\
x=-9 [/tex]
Therefore, first option gives the correct answer
