1. We are asked to add the fractions $\frac{9}{14} + \frac{4}{12}$.\n\n2. To add fractions, we need a common denominator. The denominators are 14 and 12.\n\n3. Find the least common denominator (LCD) of 14 and 12.\n\n- Prime factors: 14 = 2 \times 7, 12 = 2^2 \times 3\n- LCD = 2^2 \times 3 \times 7 = 4 \times 3 \times 7 = 84\n\n4. Convert each fraction to have denominator 84:\n\n$$\frac{9}{14} = \frac{9 \times 6}{14 \times 6} = \frac{54}{84}$$\n$$\frac{4}{12} = \frac{4 \times 7}{12 \times 7} = \frac{28}{84}$$\n\n5. Now add the numerators:\n\n$$\frac{54}{84} + \frac{28}{84} = \frac{54 + 28}{84} = \frac{82}{84}$$\n\n6. Simplify the fraction $\frac{82}{84}$ by dividing numerator and denominator by their greatest common divisor (GCD).\n\n- GCD of 82 and 84 is 2.\n\n$$\frac{\cancel{82}^{{\color{red}41}}}{\cancel{84}^{{\color{red}42}}}$$\n\n7. Final simplified answer is:\n\n$$\frac{41}{42}$$