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Choice D is correct. The value of $g\left(x\right)$ when $x=8$ can be found by substituting $8$ for $x$ in the given equation $g\left(x\right)=10x+8$. This yields $g\left(8\right)=10\left(8\right)+8$, or $g\left(8\right)=88$. Therefore, when $x=8$, the value of $g\left(x\right)$ is $88$.

Choice A is incorrect. This is the value of $x$ when $g\left(x\right)=8$, rather than the value of $g\left(x\right)$ when $x=8$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.