\(\lim\limits_{x\rightarrow6+}f\left(x\right)=\lim\limits_{x\rightarrow6+}\dfrac{x^2-36}{x-6}=\lim\limits_{x\rightarrow6+}x+6=12\)
\(\lim\limits_{x\rightarrow6-}f\left(x\right)=\lim\limits_{x\rightarrow6-}4x-12=12\)
\(\Rightarrow\lim\limits_{x\rightarrow6}f\left(x\right)=\lim\limits_{x\rightarrow6+}f\left(x\right)=\lim\limits_{x\rightarrow6-}f\left(x\right)=12\)