Answer
The three organelles that are involved in protein synthesis are the ribosomes, rough endoplasmic reticulum, and the golgi complex.
Work Step by Step
You may include the nucleus in this list since the nucleus contains the DNA for protein synthesis.
Ribosomes read mRNA and assemble amino acids into proteins. There are often many ribosomes in the rough ER (it's what makes it look "rough"). The rough ER also synthesizes proteins for the plasma membrane and to be excreted out of the cell. The Golgi complex puts the finishing touches on protein synthesis.