The answer, 2c = 4x-16, is correct, though I can't be sure of the thinking that arrived at it.
I would not normally expect a beginner to be using three variables (c, p, x), but in fact that is perhaps the easiest way. What I would have done here is to multiply the first equation by 4: 4c + 4p = 4x, and subtract the second equation from that: (4c + 4p) - (2c + 4p) = 4x - 16, and the left-hand side reduces to 2c.
I was expecting the same thing but without the variables: if one of each costs a total of x dollars, then 4 of each costs 4 x; 2 calculators and 4 pens is $16, and the difference is the cost of the extra two calculators. Using letters instead of words amounts to the same thing, but easier to say!