In order to distribute be sure to use the F.O.I.L method! Here's my work to help:
FOIL = first, outer, inner, last
1. (x-2)(2x+3)--- multiply the first values in both parentheses to get 2x^2.
2. Multiply the outer values (x and 3) to get 3x
3. Multiply the inner values (-2 and 2x) to get -4x
4. Multiply the last values (3 and -2) to get -6.
5. Place all the values together and then simplify by combining like terms...
2x^2 -3x - 4x -6 which simplifies to your final answer of 2x^2-x-6. Hope this helped :))