Let's solve each of the problems using the digits 3, 4, 6, and 8 exactly once in each equation while following the PMDAS rule (Parentheses, Multiplication and Division, Addition and Subtraction).

1. (___ + ) ÷ ( + ___) = 2

   Solution: $(6 + 4) ÷ (8 + 2) = 10 ÷ 5 = 2$ This does not work, let's try: $(8 + 4) ÷ (6 + 2) = 12 ÷ 6 = 2$ This works!

2. ___ + (___ ÷ ___) x ___ = 12

   Solution: $3 + (6 ÷ 2) x 4$

3. ___ x ___ x ___ ÷ ___ = 9

   Solution: $6 x 3 x 2 ÷ 4$

4. ___ x (___ x ___) ÷ ___ = 16

   Solution: $3 x (4 x 2) ÷ 6$

5. ___ ÷ (___ ÷ ___) + ___ = 7

   Solution: $8 ÷ (3 ÷ 6)$