jmc

Without parentheses, the expression has the value (following order of operations) $8+(4\times 6)/2=20$. The parentheses can modify the order of operations, either through $(8+4)\times 6÷2=36$ or $(8+4\times 6)/2=16$, giving $\boxed{3}$ distinct values. (Note that placing parentheses that exclude the first number doesn't affect the result, since the only important order of operations here is multiplication before addition.)