Let's simplify both the numerator and the denominator separately first.

Numerator:
3√8 = 3 √4 √2 = 3 2 √2 = 6√2
2√12 = 2 √4 √3 = 2 2 √3 = 4√3
√20 = √4 * √5 = 2√5

Therefore, the numerator simplifies to:
6√2 - 4√3 - 2√5

Denominator:
3√18 = 3 √9 √2 = 3 3 √2 = 9√2
2√27 = 2 √9 √3 = 2 3 √3 = 6√3
√45 = √9 * √5 = 3√5

Therefore, the denominator simplifies to:
9√2 - 6√3 - 3√5

Now, substitute the simplified numerator and denominator back into the expression:

(6√2 - 4√3 - 2√5) / (9√2 - 6√3 - 3√5)

This expression cannot be simplified further, so the final simplified form of the expression is:
(6√2 - 4√3 - 2√5) / (9√2 - 6√3 - 3√5)