1. Identify the common factor in all terms: The terms are -2xy, -4x^2, and 6x. The common factor is -2x.
2. Factor out the common factor -2x:
-2xy - 4x^2 + 6x = -2x(y) - 2x(2x) + 2x(-3)
3. Simplify the expression:
-2x(y + 2x - 3)
The factored form is -2x(y + 2x - 3).