To subtract the fractions \( \frac{1}{4} \) and \( \frac{1}{6} \), we first need to find a common denominator. The least common multiple of 4 and 6 is 12.
Next, we convert each fraction to have a denominator of 12:
\[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \]
\[ \frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12} \]
Now, we can subtract the two fractions:
\[ \frac{3}{12} - \frac{2}{12} = \frac{3 - 2}{12} = \frac{1}{12} \]
Thus, \( \frac{1}{4} - \frac{1}{6} \) in simplest form is
\[ \boxed{\frac{1}{12}} \]