Step 1 :The expression $(g \circ f)(3)$ represents the composition of two functions, $g$ and $f$.
Step 2 :To evaluate this expression, we first find the value of $f(3)$ from the table, which is 6.
Step 3 :We then substitute this value into $g(x)$, so we need to find the value of $g(6)$ from the table, which is 7.
Step 4 :So, $(g \circ f)(3)=g(f(3))=g(6)=7$
Step 5 :Final Answer: $(g \circ f)(3)=\boxed{7}$