1. **Problem statement:** Find the coordinates of point P which is 5 cm from BC and 4 cm from A's altitude in rectangle ABCD with AB = 8 cm and BC = 6 cm. 2. **Formula and rules:** The distance from a point to a line is the perpendicular length from the point to the line. We use the coordinate system placing A at origin (0,0), AB along x-axis, BC along y-axis. 3. **Set coordinates:** Let A = (0,0), B = (8,0), C = (8,6), D = (0,6). 4. **Distance from BC:** BC is the vertical line x=8. Distance from point P = (x,y) to BC is $|x-8|$. 5. **Distance from A's altitude:** The altitude from A is the vertical line x=0. Distance from P to this line is $|x-0|=|x|$. 6. **Given distances:** Distance to BC is 5 cm, so $|x-8|=5$. 7. **Solve for x:** $|x-8|=5$ gives two solutions: $x=8-5=3$ or $x=8+5=13$. 8. **Distance to A's altitude is 4 cm:** $|x|=4$ gives $x=4$ or $x=-4$. 9. **Find common x:** From step 7, x=3 or 13; from step 8, x=4 or -4. No common x, so interpret "A's altitude" as the horizontal distance from A along y-axis. 10. **Altitude from A is vertical line AB (y=0), so distance from P to AB is $|y-0|=|y|$. 11. **Distance to AB is 4 cm:** $|y|=4$ so $y=4$ or $y=-4$ (only positive inside rectangle, so y=4). 12. **Distance to BC is 5 cm:** $|x-8|=5$ so $x=3$ or $x=13$ (13 outside rectangle, so x=3). 13. **Coordinates of P:** $(3,4)$. 14. **Final answer:** Point P is at coordinates $\boxed{(3,4)}$ cm inside rectangle ABCD.