To add the fractions \( \frac{2}{3} \) and \( -\frac{5}{12} \), you need to find a common denominator. The least common denominator (LCD) of 3 and 12 is 12.

First, convert \( \frac{2}{3} \) to a fraction with a denominator of 12:

\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]

Now you can add \( \frac{8}{12} \) and \( -\frac{5}{12} \):

\[ \frac{8}{12} + (-\frac{5}{12}) = \frac{8 - 5}{12} = \frac{3}{12} \]

Simplify \( \frac{3}{12} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

\[ \frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4} \]

So, \( \frac{2}{3} + (-\frac{5}{12}) = \frac{1}{4} \).