Saturated fatty acids containing up to 16 carbon atoms are assembled in
Cytoplasm

The end product of cytosolic fatty acid synthesis cycles is saturated 16-carbon palmitic acid.
Elongation of pre-existing fatty acid :-
(i) Microsomnal (endoplasmic reticulum) :- Elongation of palmitic acid (16-C) into longer chain fatty acids
(ii) Mitochondrial :- Elongation of short and medium chain fatty acids containing fewer than 16 carbon atoms
Mitochondria
Rough endoplasmic reticulum
Smooth endoplasmic reticulum
Cytoplasm