Hopefully, I can bridge the gap between the intent of the person who originally asked the question and interpretation of the question derived by the folks who left exasperated comments.
To set the record straight, the following sentence is grammatically correct,
I'll do the plumbing for free
but is improperly constructed, which leaves the interpretation of the sentence ambiguous. If you were to use this sentence in an English paper, your teacher would not mark you for improper grammar but would have an "amb" (for ambiguous) notated at the top of the sentence.
To all the negative vote givers and exasperated comment-writers who believe that there's nothing wrong with "do", you're right too!
So, what's wrong with the sentence? It's the fact that "the plumbing" is ambiguous in a written context.
In vernacular english, we automatically correct the sentence to read as follows as in our mind,
"I'll do the plumbing work for free"
In this case, the verb "do" describes "the work", wherein the kind of work involved is plumbing.
In fact, we omit the actual work described by do so commonly, that the following sentences are accepted as correct in vernacular english,
"I'll do the dishes for free" -> "I'll clean the dishes for free" or "I'll do the dish cleaning for free"
"I'll do the lawn for a penny" -> "I'll mow the lawn for free" or "I'll do the lawn trimming for free"
Why? Simple. Dishes are meant to be cleaned and lawns are meant to mowed.
- Right? Sure if the context is clear.
- Wrong? If the context is unclear.
Let's imagine for a second, a completely foreign made-up culture wherein it's custom for one person to break dishes after eating and for another person to clean the dishes are eating.
Well, it would be really confusing for them if you said, "I'll do the dishes for free", err, you mean break them or clean them?
So to get back to the original question, when you say, "I'll do the plumbing for free", you're automatically implying that "plumbing" as an adjective only modifies "work" as the noun, so you omit work and make plumbing the noun.
Hope this helps!