1. The problem is to multiply the fractions $\frac{3}{68}$ and $\frac{11}{2}$. 2. The formula for multiplying fractions is: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. Applying the formula: $$\frac{3}{68} \times \frac{11}{2} = \frac{3 \times 11}{68 \times 2} = \frac{33}{136}$$ 4. Check if the fraction $\frac{33}{136}$ can be simplified by finding the greatest common divisor (GCD) of 33 and 136. 5. The factors of 33 are 1, 3, 11, 33. 6. The factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136. 7. The GCD is 1, so the fraction $\frac{33}{136}$ is already in simplest form. 8. Therefore, the final answer is $\frac{33}{136}$.