During protein production the instructions to make the hormones are in the DNA in the nucleus.
1st stage of protein production is the nucleus copies the instructions in the DNA into a molecule called mRNA.
Stage 2 is the mRNA molecule leaves the nucleus through nuclear pores and attaches to a ribosome. In this case, the ribosome is attached to rough endoplasmic reticulum.
Stage 3 is the ribosome reads the instructions and uses the codes to assemble the hormone (protein).
Stage 4 the assembled protein inside the rough ER is pinched off in a vesicle and transported to the Golgi apparatus.
Stage 5 the Golgi body packages the protein/may modify it so it's ready for release. The protein is now packaged into a vesicle and moves to the cell surface membrane, to be where it is secreted outside.