Is it obligatory for someone who vowed to fast for two consecutive months, and is 16 years old, to do so, especially if he is unable to fast them?

A vow contingent on the occurrence of something is disliked because it extracts from a miserly person. If it is made by an adult, it becomes binding and must be fulfilled, due to the generality of Allah’s statement: {And let them fulfill their vows} (22:29), and the Prophet's (peace be upon him) saying: "Whoever vows to obey Allah, let him obey Him." As for the vow of a minor, it becomes binding if he comprehends the act of devotion, but he is not obligated to fulfill it. Rather, it is recommended for him to fulfill it after reaching puberty.