Not sure how to show work,?

Let’s do this with the a and b first:

4a² – 3ab +8ab -6b²

which is

4a² + 5ab -6b²

Now replace the a and b with √6 and √2, respectively:

4*√6² +5(√6*√2) -6*√2²

Since the square root of any number squared is itself, and √6*√2 = √12, we get

4*6 +5√12 -6*2

which is 24+5√12 -12

or

12+5√12

which is 12 + 5√(4*3)

or

12 + 10√3

If you don’t agree with the a/b method, you can do use the FOIL method, which says to multiple the First pair of numbers, then the Outside pair of numbers, then the Inside pair of numbers, then the last pair of numbers:

First Outside Inside Last

(√6)(4√6) (√6)(-3√2) (2√2)(4√6) (2√2)(-3√2)

4√36 -3√12 +8√12 -6√4

4*6 -3(√4)(√3) +8(√4)(√3) -6*2

24 (-3)(2)(√3) +8(2)(√3) -12

(24-12) -6(√3) + 16(√3)

12 + 10(√3)