To solve the expression \(-\frac{12}{7} + \frac{3}{14}\), we first need to find a common denominator.
The denominators are 7 and 14. The least common denominator (LCD) is 14.
Now we can rewrite \(-\frac{12}{7}\) with the denominator of 14:
\[ -\frac{12}{7} = -\frac{12 \times 2}{7 \times 2} = -\frac{24}{14} \]
Now we can add the two fractions:
\[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \]
Now, we can simplify \(\frac{-21}{14}\):
\[ \frac{-21}{14} = \frac{-21 \div 7}{14 \div 7} = \frac{-3}{2} \]
Thus, the final result is:
\[ -\frac{3}{2} \]