1. **State the problem:** Solve the equation $2x:5 - x:3 = 4$. 2. **Rewrite the problem with clearer notation:** The colon ":" here represents division, so the equation is $\frac{2x}{5} - \frac{x}{3} = 4$. 3. **Find a common denominator to combine the fractions:** The denominators are 5 and 3, so the least common denominator (LCD) is 15. 4. **Rewrite each fraction with denominator 15:** $$\frac{2x}{5} = \frac{2x \times 3}{5 \times 3} = \frac{6x}{15}$$ $$\frac{x}{3} = \frac{x \times 5}{3 \times 5} = \frac{5x}{15}$$ 5. **Substitute back into the equation:** $$\frac{6x}{15} - \frac{5x}{15} = 4$$ 6. **Combine the fractions:** $$\frac{6x - 5x}{15} = 4$$ $$\frac{x}{15} = 4$$ 7. **Solve for $x$ by multiplying both sides by 15:** $$\cancel{15} \times \frac{x}{\cancel{15}} = 4 \times 15$$ $$x = 60$$ **Final answer:** $x = 60$