1. The problem is to plot the point $P(3, 4, -4)$ in a three-dimensional coordinate system. 2. The point $P$ has coordinates $x=3$, $y=4$, and $z=-4$. 3. To plot this point, start at the origin $(0,0,0)$. 4. Move 3 units along the $x$-axis. 5. From there, move 4 units along the $y$-axis. 6. Finally, move down 4 units along the $z$-axis (since $z$ is negative). 7. The location you reach is the point $P(3,4,-4)$. 8. This point can be visualized in 3D space as a single dot at those coordinates. Final answer: The point $P$ is located at $(3,4,-4)$ in 3D space.