1. **Problem statement:** Given a geometric figure with points Q, B, S, and H, and lengths QB = 3m and QS = 4m, find the difference in length between SH and BH. 2. **Understanding the problem:** We need to find $|SH - BH|$. 3. **Assumptions and approach:** Since the problem does not provide explicit information about points H or the relationships between these points, we assume H lies on the segment BS or QS. We use the given lengths and properties of triangles or line segments to express SH and BH. 4. **Using the triangle inequality or segment addition:** If H lies between B and S, then $BS = BH + HS$. 5. **Calculate BS:** Using points Q, B, and S, if Q is a point such that QB = 3m and QS = 4m, then by the Pythagorean theorem, if Q, B, S form a right triangle with right angle at B or S, $BS = \sqrt{QS^2 - QB^2} = \sqrt{4^2 - 3^2} = \sqrt{16 - 9} = \sqrt{7}$ meters. 6. **Express difference:** Since $BS = BH + HS$, then $|SH - BH| = |BS - 2BH|$. 7. **Without additional info about H, the difference $|SH - BH|$ equals the length $QB = 3m$ or $QS = 4m$ depending on H's position. Since the problem asks for the difference, and given the data, the difference is 1m. **Final answer:** $$\boxed{1\text{ meter}}$$