To add the fractions \(-\frac{12}{7}\) and \(\frac{3}{14}\), we need to find a common denominator.
The denominators are 7 and 14. The least common denominator (LCD) is 14.
Now, let's convert \(-\frac{12}{7}\) to a fraction with a denominator of 14:
\[ -\frac{12}{7} = -\frac{12 \times 2}{7 \times 2} = -\frac{24}{14} \]
Now we can add the two fractions:
\[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \]
Next, we will reduce \(\frac{-21}{14}\). The greatest common divisor (GCD) of 21 and 14 is 7.
Now, divide both the numerator and denominator by their GCD:
\[ \frac{-21 \div 7}{14 \div 7} = \frac{-3}{2} \]
Therefore, the answer is:
\[ \boxed{-\frac{3}{2}} \]