To simplify the expression (3xy/x-y) * (x-y/6xy²), we can first simplify each part separately:

(3xy/x-y):
= (3xy) / (x-y)
= (3xy) / (x-y)
= 3y

(x-y/6xy²):
= (x-y) / (6xy²)
= (x-y) / (6xy²)
= (x-y) / (6xy²)
= 1 / (6y)

Therefore, the simplified expression is:
3y * (1 / (6y))
= 1 / 2

Now, for the expression (3ab³/a-b)²:(6ab^4):

(3ab³/a-b)²:
= (3ab³ / (a - b))²
= (3ab³ / (a - b)) * (3ab³ / (a - b))
= (9a²b⁶) / (a - b)²

Next, we divide the expression by (6ab^4):
= ((9a²b⁶) / (a - b)²) / (6ab^4)
= (9a²b⁶) / (6ab^5) [When dividing by a term, we subtract the exponents]
= (3/2)b

So, the final simplified expression is:
(3a²) / 2