Only the matrix clause in a sentence requires subject-auxiliary inversion to make it interrogative (and not if the wh-word is part of a Subject phrase). In other words, all other things being equal, we use subject-auxiliary inversion to mark sentences, not subordinate clauses as interrogative.
We only use the auxiliary DO, when some grammatical operation or construction requires an auxiliary and we do not already have one in the canonical version of the sentence.
In the sentence above the Subject is the noun phrase her elephant. The word can is an auxiliary verb taking the verb dance as a Complement. If we want to turn this sentence into a canonical interrogative sentence to make a question, then we need to do a very simple operation on it. We need to invert the Subject and the auxiliary verb:
If we want to make the sentence emphatic, we stress the auxiliary verb:
Let's look at a different type of sentence:
- My elephant ate five donuts.
This sentence is different because it has no auxiliary verb. It has the verb ate as the Head of the Predicate. Also it contains a Direct Object, five donuts. This Object consists of a noun phrase. It has the noun donuts as its Head and the numeral five in Determiner function. Now suppose we want to make this sentence emphatic. To do this we need to stress the auxiliary verb. This is problematic because there is no auxiliary verb. In situations like this we insert the dummy auxiliary DO to give us an auxiliary to stress:
- My elephant did eat five donuts.
Ok, so now let's assume that we want to change the sentence into a question. We want the undetermined part of the question to refer to the numeral:
- My elephant ate [how many] donuts?
To turn this into a canonical question, we need to move the interrogative word to the front of the question. Because the question word appears within a noun phrase, the whole noun phrase must move to the front of the sentence:
- *How many donuts my elephant ate? (ungrammatical)
However, this is not enough. We still need to invert the Subject and the auxiliary verb. We have the same problem we had when we wanted to make the sentence emphatic. There's no auxiliary to invert. Again we will need to insert DO:
- How many donuts did my elephant eat?
We can embed interrogative clauses as the complements of other verbs:
- She will ask [how many donuts my elephant ate].
- Will she ask [how many donuts my elephants ate]?
Notice that the bracketed subordinate interrogative clauses here do not exhibit subject auxiliary inversion. They are like our ungrammatical question how many donuts my elephant ate?. There is an important difference between the two sentences above. The first sentence is a declarative sentence used as a statement. The second is an interrogative sentence used as a question. Notice that we only need to use subject-auxiliary inversion in the main (technically the matrix) clause. In other words subject-auxiliary inversion is only required to turn the whole sentence into an interrogative clause. We don't need to use subject-auxiliary inversion in subordinate interrogative clauses. In the sentences above, because we do not need subject-auxiliary inversion in the subordinate clause, we do not need to insert the dummy auxiliary DO.
However, we might still want to make the subordinate clause emphatic. For example, we might want to contrast it with an incorrect idea that has been previously mentioned:
A: You incorrectly stated that my elephant ate five donuts.
B: Could you tell me how many donuts your elephant did eat?
Here we have inserted the dummy auxiliary DO to make the subordinate clause emphatic. Notice that the word do is coming after the Subject here, not before it. The do insertion is for emphasis, not because this subordinate clause is interrogative.
The Original Poster's example
- Could you tell me how many people you have?
- Could you tell me how many people you do have?
The first example above is the normal way to phrase this sentence. The subordinate interrogative clause "how many people you have" does not require subject-auxiliary inversion and therefore we do not need to use the auxiliary DO to make the clause interrogative.
The second example, however, is also grammatical. It makes the subordinate clause emphatic. Notice that this has nothing to do with the clause being interrogative. The do is being inserted to give us an auxiliary to stress. Notice as well that
the auxiliary do comes after the Subject, not before it.