Let's solve these two problems step-by-step:

Question 11: $(f \circ g)(6)$

1. Understand the composition: $(f \circ g)(x)$ means $f(g(x))$. First, find $g(6)$ and then substitute it into $f(x)$.
2. Locate $g(6)$:
   • From the $g(x)$ row, when $x = 6$, $g(6) = 4$.
3. Substitute $g(6)$ into $f(x)$:
   • Now, find $f(4)$ using the $f(x)$ row. When $x = 4$, $f(4) = 6$.
4. Final answer: $(f \circ g)(6) = 6$.

Question 12: $(f \circ f)(5)$

1. Understand the composition: $(f \circ f)(x)$ means $f(f(x))$. First, find $f(5)$ and then substitute it into $f(x)$.
2. Locate $f(5)$:
   • From the $f(x)$ row, when $x = 5$, $f(5) = 2$.
3. Substitute $f(5)$ into $f(x)$:
   • Now, find $f(2)$ using the $f(x)$ row. When $x = 2$, $f(2) = 3$.
4. Final answer: $(f \circ f)(5) = 3$.

Let me know if you'd like detailed explanations for any part! Here are some related questions to expand your understanding:

1. How do you compute the composition of three functions, e.g., $(f \circ g \circ h)(x)$?
2. What is the significance of the order of composition in functions?
3. How does function composition differ from standard addition or multiplication of functions?
4. Can compositions like $(g \circ g)(x)$ ever result in undefined values?
5. What happens if one of the functions is a constant function (e.g., $g(x) = c$)?

Tip: Always start from the innermost function when evaluating compositions. This ensures accuracy and logical order!