1. **State the problem:** We need to find the composition of functions $f$ and $g$, denoted as $(f \circ g)(x)$, which means $f(g(x))$. 2. **Recall the functions:** $$f(x) = 4x - 2$$ $$g(x) = x^2 + 4x$$ 3. **Apply the composition:** Substitute $g(x)$ into $f$: $$ (f \circ g)(x) = f(g(x)) = f(x^2 + 4x) $$ 4. **Use the formula for $f(x)$:** Replace $x$ in $f(x)$ with $x^2 + 4x$: $$ f(x^2 + 4x) = 4(x^2 + 4x) - 2 $$ 5. **Simplify the expression:** $$ 4(x^2 + 4x) - 2 = 4x^2 + 16x - 2 $$ 6. **Restrictions on the variable:** Since $f$ and $g$ are polynomials, there are no restrictions on $x$; $x$ can be any real number. **Final answer:** $$(f \circ g)(x) = 4x^2 + 16x - 2$$