Once you have $\dfrac{2}{p} = 1 - \dfrac{3}{q}$, rewrite $1$ as a fraction with denominator $q$ so you can combine it with $-\dfrac{3}{q}$.

After combining, you should get one fraction on each side. When you have $\dfrac{2}{p} = \dfrac{\text{something}}{\text{something}}$, what operation lets you clear the denominators in one step?

After cross-multiplying, you will have $p$ multiplied by some expression in $q$. How do you undo that multiplication to leave $p$ by itself?

Choose a simple positive value for $q$ that does not make any denominator zero, such as $q = 4$. You can change this later to a different value like $q = 5$ to double-check.

For each answer choice, type an expression in Desmos like pA = 2*4/(4-3), pB = 2*4/(4+3), etc., using your chosen value of $q$. Desmos will give you a numerical value of $p$ for each option.

For each computed $p$ value, type 2/pA + 3/4, 2/pB + 3/4, and so on. Look at Desmos’s output and see which option makes the value of 2/p + 3/q equal to exactly 1.

Repeat the same process with a different positive $q$ (for example, $q = 5$). The correct expression for $p$ will make 2/p + 3/q equal to 1 for every valid $q$ you test, while the incorrect ones will not.

Start with

Subtract $\dfrac{3}{q}$ from both sides to get

Now all the $p$ terms are on one side of the equation.

Write $1$ as $\dfrac{q}{q}$ so you can combine the fractions:

Now the equation is

This is a proportion (one fraction equals another).

From

cross-multiply:

Now divide both sides by $q-3$ (note $q \ne 3$ so this is allowed):

So the correct equation expressing $p$ in terms of $q$ is $p = \dfrac{2q}{q-3}$.