$\frac{3 g^{2}+12 g}{g+7} \cdot \frac{4}{8 g^{2}}$
Final Answer: \(\boxed{\frac{3(g + 4)}{2g(g + 7)}}\)
Step 1 :Simplify the expression inside the first fraction: \(\frac{3 g^{2}+12 g}{g+7}\)
Step 2 :Simplify the expression inside the second fraction: \(\frac{4}{8 g^{2}}\)
Step 3 :Multiply the two simplified fractions: \(\frac{3 g^{2}+12 g}{g+7} \cdot \frac{4}{8 g^{2}}\)
Step 4 :Final Answer: \(\boxed{\frac{3(g + 4)}{2g(g + 7)}}\)