we have constant term for both p and q.
while p is +ve and q is -ve
we can add the two eqn to get,
10p = 60
that reduces to p = 6

put 6 for p in any of the two eqn to get
q=-4
we have to add the absolute value of both p and q
we have the +ve value of p for q we need to take the absolute value of q as 4
hence |p|+|q| = 10

Given that 5p – 3q = 42 and 5p + 3q = 18 and we need to find the value of |p| + |q|

Let's start by solving the two equations and getting the value of p and q

5p – 3q = 42 ...(1)
5p + 3q = 18 ...(2)

Adding (1) and (2) we get
5p – 3q + 5p + 3q = 42+18
=> 10p = 60
=> p = \(\frac{60}{10}\) = 6

(2) - (1) we get
5p + 3q - (5p – 3q ) = 18 - 42
=> 5p + 3q - 5p + 3q = -24
=> 6q = -24
=> q = \(\frac{-24}{6}\) = -4

=> |p| + |q| = |6| + |-4| = 6 + 4 = 10

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Absolute Values