To simplify the given expression, we can first expand each of the terms and then combine like terms:

Expanding (y-2)(y+1):
(y-2)(y+1) = y² + y - 2

Expanding 18(y-3)(y+1):
18(y-3)(y+1) = 18(y² - 2y - 3) = 18y² - 36y - 54

Expanding -18(y-3)(y+2):
-18(y-3)(y+2) = -18(y² - y - 6) = -18y² + 18y + 108

Now, combining the expanded terms:
(y² + y - 2) + (18y² - 36y - 54) - (18y² + 18y + 108)
= y² + y - 2 + 18y² - 36y - 54 - 18y² - 18y - 108
= y² + 18y² - 18y² + y - 36y + 18y - 2 - 54 - 108
= y - 72

Therefore, (y-2)(y+1) + 18(y-3)(y+1) - 18(y-3)(y+2) simplifies to y - 72.