The organelle that can be either bound to the endoplasmic reticulum (ER) or free in the cytoplasm and functions in protein synthesis is the ribosome.

Here's a breakdown:

* Bound ribosomes: These are attached to the ER membrane and synthesize proteins destined for export outside the cell, incorporation into membranes, or entry into certain organelles.

* Free ribosomes: These float in the cytoplasm and synthesize proteins that will function within the cytoplasm.

While both types of ribosomes have the same basic structure, their location dictates the fate of the proteins they produce.