Step-by-step explanation:
We can translate the sentence hace tres meses que conozco a Juan into I've known Juan for three months. So the group of words hace tres meses comes from a common formula in Spanish:
Hace + number + días/meses/años
that is used to tell you something has happened from the past until now. If the number is uno (one), días/meses/años (plural form) changes to día/mes/año (singular form)