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The correct answer is $11$ or $-7$. By the definition of absolute value, if $\left(x-2\right)=9$, then $x-2=9$ or $x-2=-9$. Adding $2$ to both sides of the equation $x-2=9$ yields $x=11$. Adding $2$ to both sides of the equation $x-2=-9$ yields $x=-7$. Thus, the given equation, $\left(x-2\right)=9$, has two possible solutions, $11$ and $-7$. Note that 11 and -7 are examples of ways to enter a correct answer.