APPROACH #1: Algebra
This is a matter of simplifying like terms.
Here's an example: 3x + 4x = (3 + 4)x = 7x

Likewise: x(x–y) – z(x–y) = (x - z)(x–y)

Answer: C

-----------------------------------------------------
APPROACH #2: Test values
We're looking for an expression that is EQUIVALENT to x(x – y) – z(x – y)
So, for any set of values for x, y and z, the correct answer must evaluate to have the same value as x(x – y) – z(x – y)

So, let's plug in some values for x, y and z
Let's try x = 3, y = 1 and z = 10

First plug those values into the GIVEN expression.
We get: x(x – y) – z(x – y) = 3(3 – 1) – 10(3 – 1)
= 3(2) – 10(2)
= 6 - 20
= -14

So, the correct answer choice will be the one that evaluates to -14 when we plug in x = 3, y = 1 and z = 10
(A) x – y = 3 - 1 = 2. We want -14. ELIMINATE A
(B) x – z = 3 - 10 = -7. We want -14. ELIMINATE B
(C) (x – y)(x – z) = (3 - 1)(3 - 10) = (2)(-7) = -14. GREAT! KEEP C
(D) (x – y)(x + z) = (3 - 1)(3 + 10) = (2)(13)= 26. We want -14. ELIMINATE D
(E) (x – y)(z – x) = (3 - 1)(10 - 3) = (2)(7)= 14. We want -14. ELIMINATE E

By the process of elimination, the correct answer is C

Cheers,
Brent