f = # of 4-student tables
s = # six-student tables
4f + 6s = 32
2f + 3s = 16
Now, 2f is even, so 3f must be even to add to 32, an even number. So, s must be even.
(f,s) = (2,4),(5,2)
since there are an odd number of tables,
5 seat 4 students, 2 seat six students.