The use of specifically here is unusual.
Specifically (and specific) can be used as a synonym for in detail or it can be used to ask for clarification about which thing of many is being referred to.
You haven't been clear on how you got from here to there. What did you do, specifically?
You've told about five things you like for breakfast. Which specific one would you like to eat this morning?
Neither of those apply in any of these sentences. Also, the use of specifically with how what and how have been combined makes the sentences a bit awkward.
If you don't know anything about a machine, you wouldn't know that it measures things in the first place. So, you might ask what it does, specifically, not how it does it or to what—although those details might emerge from a specific answer to what.
You asked if we would write the sentence in another way. You also provided clarification to the question in a comment by saying, "there are a group of possible things the equipment could measure."
I would say that a better phrasing would be something like the following:
Which of those things, specifically, does the equipment measure, and how does it do that?
Our aim is to understand which of those things, specifically, the equipment measures, and how it does so.
By adding "those things," the use of specifically makes more sense. So long as they have been mentioned previously, or its understood in some other way what they are, then the sentence is fine. (But if all we had to go on were the standalone sentence, then it wouldn't be clear what they were.)
You can express this in a more general way, but it will lack more context. It would also sound better if you used the variant of the word.
Our aim is to understand what specific things the equipment measures, and how it does so.