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The correct answer is $11$. It's given that $f\left(x\right)$ is defined by the equation $f\left(x\right)=mx-28$, where $m$ is a constant. It's also given in the table that when $x=10$, $f\left(x\right)=82$. Substituting $10$ for $x$ and $82$ for $f\left(x\right)$ in the equation $f\left(x\right)=mx-28$ yields, $82=m\left(10\right)-28$. Adding $28$ to both sides of this equation yields $110=10m$. Dividing both sides of this equation by $10$ yields $11=m$. Therefore, the value of $m$ is $11$.