On option is to apply the input-output approach

Let's see what happens when p = 4

The question becomes:
How many integers are greater than 2(4) and less than 4(4) − 1?
In other words, How many integers are greater than 8 and less than 15?
The integers are 9, 10, 11, 12, 13 and 14 (6 integers)
So, when p = 4, the answer to the question is 6

Now we'll check each answer choice to see which one yields an OUTPUT of 6 when we INPUT p = 4

A. p/2 = 4/2 = 2. No good. We want an output of 6

B. p = 4 = 4. No good. We want an output of 6

C. p+1 = 4 + 1 = 5. No good. We want an output of 6

D. 2p-2 = 2(4) - 2 = 6. PERFECT!

E. 3p-3 = 3(4) - 3 = 9. No good. We want an output of 6

Answer: D