This is a tricky one because there is a phrasal verb "to carry out" which means "to do something important" or "to do something that you have said you would do."

However, if you write this as one word (carryout) or with a hyphen (carry-out), it becomes a noun or an adjective with a meaning about food that is bought from a restaurant but taken elsewhere to eat.

Take-out and takeout have the same meaning as carry-out and carryout -- and none of these are verbs. 

The last word in all of the following sentences is a noun:

I want to order food for carry-out.

I want to order food for carryout.

I want to order food for take-out.

I want to order food for takeout.

I want to order food for delivery.

“Carryout” here is a noun and is spelled as one word (or with a hyphen). It denotes the action of carrying something out. You can also say “takeout”, and again, it's spelled as one word.

You can replace it with “delivery” to make this clearer: “I want to order food for delivery.” It's the same sentence structure, and “delivery“ is a noun denoting the action of delivering something.