To factor the expression x^2 - xy - 6x + 6y, we can group the terms:

(x^2 - xy) - (6x - 6y)

Now, let's factor out the common factors from each group:

x(x - y) - 6(x - y)

Notice that we have a common factor of (x - y) in both terms. We can factor this out:

(x - y)(x - 6)

Therefore, the factored form of the expression x^2 - xy - 6x + 6y is (x - y)(x - 6).