Which sentence shows correct subject- verb agreement?
a. my friend and her mother were listening to the radio.
b. my friend and her mother was listening to the radio.

A is correct because "my friend and her mother" can be substituted by the pronoun "they" which is plural, therefore the plural verb needs to be used, which is "were".

A  is correct. this is because more than one person was listening to the radio (my friend AND her mom) so you would use were as a plural tense rather than was because was refers to only one person using the radio.
i hope this helped