1. The problem asks us to find the composition of functions $f$ and $g$, denoted as $(f \circ g)(x)$, which means $f(g(x))$. 2. Given $f(x) = 2x + 3$ and $g(x) = 4x^{2} + 3x$, the composition is: $$ (f \circ g)(x) = f(g(x)) = f\left(4x^{2} + 3x\right) $$ 3. Substitute $g(x)$ into $f(x)$: $$ f\left(4x^{2} + 3x\right) = 2\left(4x^{2} + 3x\right) + 3 $$ 4. Distribute the 2: $$ 2 \times 4x^{2} + 2 \times 3x + 3 = 8x^{2} + 6x + 3 $$ 5. Therefore, the simplified composition is: $$ (f \circ g)(x) = 8x^{2} + 6x + 3 $$ This means that applying $g$ first and then $f$ results in the quadratic expression $8x^{2} + 6x + 3$.