Instead of 2nd root you say "square root"
Instead of 3rd root you say "cube root"

3∛(2a)-6∛(2a)

Those are LIKE TERMS:

That's just like 

3x-6x are LIKE terms.

It's just that instead of a simple x you have a complicated  ∛(2a)

But that doesn't make the problem any more complicated.

Just as 

the answer to 3x-6x is -3x, because they are LIKE TERMS, and
you just combine coefficients 3-6 and get -3, and then put x after that,

the answer to 3∛(2a)-6∛(2a) is -3∛(2a), because they are LIKE TERMS, and
you just combine coefficients 3-6 and get -3, and then put ∛(2a) after that.

Therefore 3∛(2a)-6∛(2a) is just -3∛(2a)

Edwin