You have to work backward here. Sorry if it's confusing, idk how to properly explain this problem but hope it helps!
You would have to look at the amount of 6-person tables and start off with 6 tables and decrease a table each time until the number of people remaining is a multiple of 4.
So, 5 tables don't work because you have 6 people reaming,
But 4 tables work because you would have 12 people remaining.
So then you would have 4 6-person tables and 3 4-person tables.