The folded organelle just outside of the nucleus that is covered in ribosomes and plays a role in protein synthesis is called the
А folded Golgi Apparatus.
B smooth endoplasmic reticulum.
С membrane-bound mitochondria.
D rough endoplasmic reticulum.
The rough endoplasmic reticulum is a folded organelle inside of a cell, much like it's smooth counterpart except is covered in ribosomes, giving it the 'rough' name.