Let's simplify each term separately:

(4√2-2√3)(6√2+3√3)
= 24(√2)^2 + 12√2√3 - 12√3√2 - 6(√3)^2
= 24(2) + 12(√6) - 12(√6) - 6(3)
= 48 + 0 - 18
= 30

(1-√3)(√3+1)
= (√3) + 1 - 3 - √3
= 1 - √3 - √3
= 1 - 2√3

Now, subtract the two results:

30 - (1 - 2√3)
= 30 - 1 + 2√3
= 29 + 2√3

Therefore, the final simplified expression is 29 + 2√3.