Basically it occurs in the RIBOSOME of the cell.
Explanation ;
Now what happens is the ribosome- the protein factory of the cell has a groove at the junction of the 2 subunits.
From this groove,a tunnel extends through the large subunit and opens into the canal of the Endoplasmic reticulum.
The polypeptides synthesised in the groove between 2 subunits pass through the tunnel into the ER.(endoplasmic reticulum.)
So, protein synthesis occurs in ribosome in close association with ER & GOLGI BODIES.