I'll use the AC method

1. Multiply 4 by 6, get 24.
2. Break up 24 every possible way.
3. Since the last term -6 is negative,
   write the difference of the two factors of 24.
   [Had it been positive we would have written the 
    sum of them]

24 = 24×1, 24-1=23
24 = 12×2, 12-2=10
24 =  8×3,  8-3=5
14 =  6×4,  6-4=2

Look among the differences for the coefficient of
x (in absolute value in case it were negative)

We see that 8-3=5 and the coefficient of x is 5.

So we know to break 5x up as +8x-3x

4x²+8x-3x-6

Factor 4x out of the first two term.
Factor -3 out of the last two terms:

4x(x+2)-3(x+2)

Factor out common factor (x+2)

(4x-3)(x+2)

Edwin