1. **Stating the problem:** We have a pulley system with a mass $2m$ hanging vertically downward a distance $h$ from a fixed support on the left side. On the right side, over the pulley, there is a mass $m$ on a horizontal surface. We want to analyze or solve for relationships involving height $h$ and the motion of masses given the system. 2. **Setting up variables:** Let the vertical displacement of the heavy mass $2m$ be $h$ downward. 3. **Analyzing the string constraint:** Because the string passes over the pulley and the system is ideal (no stretch, massless pulley and string), the length of the string is constant. 4. **Relating the displacements:** If the heavy mass $2m$ moves down by $h$, then the mass $m$ on the horizontal surface must move horizontally by a distance related to $h$—since the total string length is fixed and the string passes over the pulley, the horizontal displacement $x$ of mass $m$ is equal to $h$. 5. **Conclusion:** The height $h$ that the $2m$ mass descends is equal numerically to the horizontal displacement $x$ of mass $m$, i.e. $$x=h$$. If you want further information, like the acceleration or forces, please specify.