Right answer:
a) Juego al tenis hace un mes
We can translate the sentence I have been playing tennis for a month into Juego al tenis hace un mes. So the group of words hace un mes comes from a common formula in Spanish:
Hace + number + días/meses/años
that is used to tell you something form the past until now. Since the number is uno (one), días/meses/años (plural form) changes to día/mes/año (singular form)