To simplify the expression (1/3 - 5/16) divided by (1/6 - 1/8), we first find a common denominator for each fraction within the expression.

(1/3 - 5/16) = (16/48 - 15/48) = 1/48

(1/6 - 1/8) = (4/24 - 3/24) = 1/24

Therefore, the expression simplifies to:

(1/48) / (1/24) = (1/48) * (24/1) = 24/48 = 1/2

Therefore, the final simplified expression is 1/2.