First, we need to expand each of the terms:

(√2-3)^2 = (√2-3)(√2-3)
Expanding using FOIL method:
= (√2)(√2) - 3√2 - 3√2 + 9
= 2 - 6√2 - 6√2 + 9
= 11 - 12√2

(√3-1)^2 = (√3-1)(√3-1)
Expanding using FOIL method:
= (√3)(√3) - √3 - √3 + 1
= 3 - 2√3 + 1
= 4 - 2√3

Now, multiplying the expanded terms:
(11-12√2)(11+6√2) = 121 - 66√2 + 66√2 - 72
= 49

(4-2√3)(4+2√3) = 16 - 8√3 + 8√3 - 12
= 4

Finally, multiplying the results of the two products:
49 * 4 = 196

Therefore, the result is 196.