2x-3 implies x=3/2 as a factor.
3/2 | 6 -11 11...-2
........6....9 -3...12
........6...-2..8 | 10
The result implies (x-3/2)(6x^2-2x+8) or (2x-3)(3x^2-x+4)=6x^3-11x^2+11-12+10 where 10 is the remainder. I suspect the last figure should have been -12 not -2. This would have brought the remainder to zero, and the quotient would have been 3x^2-x+4 with no remainder.