Answer: a) Peripheral slowing hypothesis.
Explanation: Peripheral slowing hypothesis is the theory that states about outer nervous system's processing and functioning speed starts to slow down. This is caused due to changes in nerves of the brain due to ageing that slows the process of communication with organs and muscles.
According to the situation of the question, Henry's slow processing of finger is due to the old age as compared to his grandson which has declined the functioning of his nerves with the muscles and organs
Other options are incorrect because generalized slowing hypothesis is slowing process of age due to cognitive factors. Reaction time shortening is the slow response .Fast speed of processing time is quick speed in processing any information for body functioning.
Thus, the correct option is option(a).