1. **State the problem:** We need to subtract $\frac{1}{6}$ from $\frac{7}{12}$.\n\n2. **Formula and rules:** To subtract fractions, they must have a common denominator. The formula is $\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$.\n\n3. **Find common denominator:** The denominators are 12 and 6. The least common denominator (LCD) is 12.\n\n4. **Convert fractions:** $\frac{7}{12}$ stays the same. Convert $\frac{1}{6}$ to twelfths: $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$.\n\n5. **Subtract:** $\frac{7}{12} - \frac{2}{12} = \frac{7 - 2}{12} = \frac{5}{12}$.\n\n6. **Final answer:** $\frac{5}{12}$ is already in simplest form.