Arachidonic acid is a 20 carbon fatty acid, so once you know the total carbon count you can work out how many of those carbons sit in the R group attached to the carboxyl end.
Counting the whole molecule as 20 carbons and setting aside the one carboxyl carbon leaves 19 carbons in the R group, so option (3) is correct.
Let's summarize:
So the R group of arachidonic acid contains 19 carbons.