To solve this inequality, we will first simplify the expression:

log⁡1/6(log2√(6-x)) > 0
log⁡(2√(6-x)) > 0
log⁡2 + log⁡√(6-x) > 0
log⁡2 + 1/2log⁡(6-x) > 0
log⁡2 + log⁡(6-x) > 0
log⁡(2(6-x)) > 0
log⁡(12-2x) > 0

Now, we will rewrite the inequality in exponential form:

12 - 2x > 1
-2x > -11
x < 11/2

Therefore, the solution to the inequality is x < 5.5.