To solve the expression \( \frac{1}{2} : \frac{1}{4} - \frac{1}{6} \), we need to follow the order of operations (PEMDAS/BODMAS). This means we first handle the division and then the subtraction.

1. **Division**: \( \frac{1}{2} : \frac{1}{4} \)

Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{1}{2} : \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{1 \times 4}{2 \times 1} = \frac{4}{2} = 2
\]

2. **Subtraction**: \( 2 - \frac{1}{6} \)

To subtract these, we need a common denominator. The common denominator for 2 (which is \( \frac{2}{1} \)) and \( \frac{1}{6} \) is 6.

Convert 2 to a fraction with a denominator of 6:
\[
2 = \frac{2 \times 6}{1 \times 6} = \frac{12}{6}
\]

Now perform the subtraction:
\[
\frac{12}{6} - \frac{1}{6} = \frac{12 - 1}{6} = \frac{11}{6}
\]

So, the result of the expression \( \frac{1}{2} : \frac{1}{4} - \frac{1}{6} \) is \( \frac{11}{6} \).