#### Answer

3y$^3$

#### Work Step by Step

First, write each number as a product of primes:
6y$^3$ = (2)(3)(y$^3$)
9y$^5$ = (3)(3)(y$^5$)
18y$^4$ = (2)(3)(3)y$^4$
To find the GCF, look for common factors between each of the factorizations. The only factor that is common between all three factorizations is the number 3. Now, look at the variables raised to powers. As all three factorizations share a y$^3$, the GCF is 3(y$^3$), which can be re-written as 3y$^3$.