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In my essay, I have a question like this:
"Why, and how does the pH level affect the resulting popping boba?"
My mom said that the comma after 'Why' was not needed, like this:
"Why and how does the pH level affect the resulting popping boba?"
Is there a difference between the two? Is one grammatically correct/incorrect?
Your mom's sentence is pretty standard:
Why and how does the pH level affect the resulting popping boba?
The interrogative adverbs "why" and "how" are connected in series. When two items are connected in series, we can make the second one nonrestrictive. In order to do so, we surround both it and the preceding conjunction with paired punctuation:
Why, and how, does the pH level affect the resulting popping boba?
Why (and how) does the pH level affect the resulting popping boba?
Why--and how--does the pH level affect the resulting popping boba?
It is fairly common to omit one of a pair of commas, but such constructions are usually clearer if you include both.
(It is also possible that ", and" separates two main clauses, the first consisting of only the word "why". However, I don't think that that is what you mean.)
With the comma it's two independent questions. The first question is just "Why?", with the details of what it's asking about omitted (this would usually be understood from the context of previous statements). The second question is "how does the pH level affect the resulting popping boba?"
Without the comma, both "why" and "how does" refer to "the pH level affect the resulting popping boba". So it's short for
Why does the pH level affect the resulting popping boba, and how does the pH level affect the resulting popping boba?
The sentence as you wrote it is grammatical but doesn't have the meaning you intended.
For example, if the context were "My popping boba tastes better when made in a copper tin. Why, and how does the pH level affect the resulting popping boba?" then the "why" question is asking why the use of a copper tin affects the flavour, while the "how" question is asking about the effect of pH.
Remove the comma: "My popping boba tastes better when made in a copper tin. Why and how does the pH level affect the resulting popping boba?" and the meaning has completely changed: now both the "why" and the "how" questions are about the effect of pH, not about the use of a copper tin.
