1. **State the problem:** We have a collection of stamps where initially the number of local stamps is $\frac{2}{3}$ of the total number of stamps. After adding 156 local stamps, the local stamps become $\frac{4}{5}$ of the new total. 2. **Define variables:** Let $x$ be the total number of stamps initially. 3. **Express initial local stamps:** The number of local stamps initially is $\frac{2}{3}x$. 4. **After adding 156 local stamps:** - New number of local stamps = $\frac{2}{3}x + 156$ - New total number of stamps = $x + 156$ 5. **Set up the equation using the new ratio:** $$\frac{\frac{2}{3}x + 156}{x + 156} = \frac{4}{5}$$ 6. **Solve the equation:** Multiply both sides by $5(x + 156)$: $$5\left(\frac{2}{3}x + 156\right) = 4(x + 156)$$ 7. **Expand both sides:** $$5 \times \frac{2}{3}x + 5 \times 156 = 4x + 4 \times 156$$ $$\frac{10}{3}x + 780 = 4x + 624$$ 8. **Bring all terms to one side:** $$\frac{10}{3}x - 4x = 624 - 780$$ 9. **Simplify left side:** $$\frac{10}{3}x - \frac{12}{3}x = -156$$ $$-\frac{2}{3}x = -156$$ 10. **Multiply both sides by $-\frac{3}{2}$ to solve for $x$:** $$x = -156 \times -\frac{3}{2}$$ $$x = 234$$ 11. **Interpretation:** There were initially 234 stamps in the collection. **Final answer:** $$\boxed{234}$$