1. **State the problem:** Calculate the value of the expression $\frac{2}{-8} + \frac{4}{9}$.\n\n2. **Recall the formula:** To add fractions, they must have a common denominator. The formula is $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$.\n\n3. **Simplify each fraction:** $\frac{2}{-8} = -\frac{1}{4}$ because dividing numerator and denominator by 2 and noting the negative sign.\n\n4. **Find common denominator:** The denominators are 4 and 9. The least common denominator (LCD) is $36$.\n\n5. **Rewrite fractions with LCD:** $-\frac{1}{4} = -\frac{9}{36}$ and $\frac{4}{9} = \frac{16}{36}$.\n\n6. **Add the fractions:** $-\frac{9}{36} + \frac{16}{36} = \frac{-9 + 16}{36} = \frac{7}{36}$.\n\n7. **Final answer:** The sum is $\frac{7}{36}$.