To transpose the equation $q = \frac{3p}{2} - 4$ and make $p$ the subject, follow these steps:

1. Add 4 to both sides to eliminate the constant on the right-hand side: $q + 4 = \frac{3p}{2}$

2. Multiply both sides by 2 to remove the fraction: $2(q + 4) = 3p$

3. Divide both sides by 3 to solve for $p$: $p = \frac{2(q + 4)}{3}$

So, the equation with $p$ as the subject is: $p = \frac{2(q + 4)}{3}$

Would you like further details on any step?

Here are some related questions:

1. How do you solve for $p$ if $q$ is given?
2. Can you simplify the equation for different values of $q$?
3. What happens if the equation has different constants, e.g., $q = \frac{5p}{3} - 7$?
4. How would you solve the equation if there was a square or square root involved?
5. How can this method be applied to more complex algebraic equations?

Tip: When transposing equations, always perform the same operation on both sides to maintain equality.