The correct option is A
1,4 addition reaction
The given reaction is a 1,4 addition reaction.
In the first step, a molecule of $$HBr$$ is added to a conjugated diene. Both $$H$$ atom and $$Br$$ atom are added to terminal $$C$$ atoms. This is 1,4 addition or conjugate addition. In the next step, the reaction with $$Mg$$ in presence of ether gives a Grignard reagent ($$R-MgX$$) which then attacks a molecule of carbon dioxide. Acid hydrolysis gives carboxylic acid.