Given that $f(x)=|x|$ and $g(x)=9 x+6$, calculate (a) $f \circ g(x)=$ (b) $g \circ f(x)=$ (c) $f \circ f(x)=$ (d) $g \circ g(x)=$

Step 1 ：First, we calculate $f(g(x))$ which is $f(9x+6)$. Since $f(x)$ is the absolute value function, we have $f(g(x)) = |9x+6|$.

Step 2 ：Next, we calculate $g(f(x))$ which is $g(|x|)$. Substituting $|x|$ into $g(x)$, we get $g(f(x)) = 9|x|+6$.

Step 3 ：Then, we calculate $f(f(x))$ which is $f(|x|)$. Since $f(x)$ is the absolute value function, we have $f(f(x)) = ||x||$, which simplifies to $|x|$.

Step 4 ：Finally, we calculate $g(g(x))$ which is $g(9x+6)$. Substituting $9x+6$ into $g(x)$, we get $g(g(x)) = 9(9x+6)+6 = 81x+60$.

Step 5 ：So, the solutions are $f(g(x)) = \boxed{|9x+6|}$, $g(f(x)) = \boxed{9|x|+6}$, $f(f(x)) = \boxed{|x|}$, and $g(g(x)) = \boxed{81x+60}$.