Question

(4-3√3)(2-√3)???? (the question marks signal the gap between the question and then me starting to distribute)

Answer 1

(4-3√3)(2-√3)
(4 - 3√3)(2 - √3) -> 4 x 2 = 8
(4 - 3√3)(2 - √3) -> -3√3 x 2 = -6√3
(4 - 3√3)(2 - √3) -> 4 x -√3 = -4√3
(4 - 3√3)(2 - √3) -> -3√3 x -√3 = 3√3 x √3 = √9√3 x √3 = √27 x √3 = √81 = 9

∴ (4-3√3)(2-√3) = 8 - 6√3 - 4√3 + 9

8 - 6√3 - 4√3 + 9
= 17 - 6√3 - 4√3
= 17 + (- 6 - 4)√3
= 17 - 10√3

Without decimals, you cannot go any further.
Tell me if I was confusing at all :)

UPDATED... AGAIN...

Answer 2

You have two binomials.  I would just FOIL them:

First:           4 x 2 = 8

Outside:  4 (-√3) = -4√3

Inside:   -3√3 (2) = -6√3

Last:   -3√3 (-√3) = 9

Addummup:  8  -  4√3  -  -6√3  +  9  =  17 - 10√3