The organelle identified in the picture as #10 the cell maintain homeostasis in what way? this organelle is the smaller white circularly shaped organelle found in the top middle of the image.

Microtubule – serves as a framework of the cell –cytoskeleton.

Nucleus – the control center of each cell. It regulates, monitors and organizes the whole cell

Since the pictures isn't given I can assume that it can be the microtubule, the microtubule is responsible for maintaing the shape and structure of the overall cell. It maintains homeostasis by permanently aiding the framework of the overall cell.
If it is the nucleus, the control center of a cell. It does a lot of functions in the cell, it helps maintain homeostasis by sending commands that the organelles do, supply energy, excrete or digest waste, regulate the movement of objects and cellular respiration, even cell division. It sustains the cell to be functional and proactive at the same time reactive to situations that is likely to occur.