To solve the proportion equation:

$\frac{4}{P} = \frac{12}{5}$

We can solve this by cross-multiplying. Cross-multiplication involves multiplying the numerator of each fraction by the denominator of the other. Here's the step-by-step process:

1. Cross-multiply: $4 \times 5 = P \times 12$
2. Simplify: $20 = 12P$
3. Solve for $P$ by dividing both sides by 12: $P = \frac{20}{12} = \frac{5}{3}$

Thus, the solution is:

$P = \frac{5}{3}$

Would you like more details on any step or have any other questions?

Here are 5 related questions to explore this concept further:

1. What is the general process for solving proportions?
2. How can we verify the solution to a proportion?
3. What happens if one of the values in the proportion is a variable?
4. How do you solve proportions involving decimals or fractions?
5. Can you solve proportions where both sides have complex expressions?

Tip: Always simplify both sides of a proportion before solving; it can make the equation easier to work with.