1. **State the problem:** Evaluate the expression $a + \frac{a b^2}{c}$ for $a=3$, $b=4$, and $c=6$. 2. **Write the formula:** The expression is given by $$a + \frac{a b^2}{c}$$ 3. **Substitute the values:** Replace $a$, $b$, and $c$ with the given numbers: $$3 + \frac{3 \times 4^2}{6}$$ 4. **Calculate powers and products:** $$4^2 = 16$$ $$3 \times 16 = 48$$ 5. **Divide and simplify:** $$\frac{48}{6} = 8$$ 6. **Add the terms:** $$3 + 8 = 11$$ **Final answer:** $$11$$