When 6x2 - 4x + 3 is subtracted from 3x2 - 2x + 3, the result is
(1) 3x2 - 2x (3) 3x2 - 6x + 6
(2) -3x2 + 2x (4) -3x2 - 6x + 6

Let's subtract then: 3x2 - 2x + 3 - (6x2 - 4x + 3)

taking out of the bracket with a changed sign: (there is a minus in front of the bracket)

3x2 - 2x + 3 - 6x2 + 4x - 3
let's reshuffle them so that similar terms are together:
3x2 - 6x2 - 2x + 4x + 3  - 3

Adding up similar terms:

-3x2 + 2x - that's our option 2!