Translation:My teacher teaches both piano and guitar.
You don't know unless other words specify it more, or from context. The famous example is たち or ら as a suffix, which specifies a group around the one mentioned. You can even add たち after a name and it means the group where the mentioned person is in. So the famous 私たち and ぼくら mean "we". かれら means "The group around him", so this means "they" (a third person and others). But the words without たち or ら can still mean one or more persons.
Because "teaches me" isn't in the Japanese sentence. This person could be your regular middle school teacher, who happens to also teach piano and guitar on the side. Or if it's a multi-talented music teacher, they could be teaching you to play the flute, but also be teaching (others) piano and guitar.
For some weird reason when I answered "My teacher teaches me the piano and guitar" it says I did it incorrectly and I didn't need the word "the" in the sentence, but then when I write "My teacher teaches me piano and guitar" it also says it's incorrect and that I needed the word "the" in there. Weird