Before answering your question, you should be aware it sounds like an order rather than a request:
Choose the correct answer, and say why
Even if we find this kind of instructions in books, it'd be better if you sounded more polite here:
- Can you help me choose the correct answer and say why? Thank you.
My only brother( ,who I love, / who I love / that I love / ,that I love, ) is an engineer.
Since "my only brother" is a well-defined noun phrase (the speaker has only one brother), a non-defining or non-restrictive relative clause (with commas) is needed. With this kind of clauses, "that" is never used. As a result, the correct sentence is:
- My only brother, who I love, is an engineer.
Since "who" is the object of the relative clause ("I love my only brother"), you can also use the more formal "whom":
- My only brother, whom I love, is an engineer.