To evaluate the expression $4c^3d$ when c=-rac{1}{2} and d=-rac{4}{3}, substitute the fractional values and evaluate the expression using the order of operations:

1. Substitute: Replace the variables with their given negative fraction values using parentheses: 4\left(-rac{1}{2} ight)^3\left(-rac{4}{3} ight).
2. Simplify exponents: Cube the fraction. A negative value raised to an odd power remains negative, so \left(-rac{1}{2} ight)^3 = -rac{1}{8}. The expression evaluates to 4\left(-rac{1}{8} ight)\left(-rac{4}{3} ight).
3. Multiply the fractions: Combine the parts into one fraction: rac{4 \cdot (-1) \cdot (-4)}{1 \cdot 8 \cdot 3}. Since there are two negative numbers being multiplied, the result will be positive.
4. Divide out common factors: The numerator becomes $16$ and the denominator $24$. Dividing out the common factor of $8$ simplifies the expression to rac{2}{3}.