The word which fills the blank is an adjective because it describes the subject, "my father". The clue lies in the words:"My father gets very angry with us whenever we make a mistake". These words describe the subject, "my father". Let us look at the meaning of each word in the given options.
The word, "tolerance" is an abstract noun which means: The ability or willingness to allow the opinions or behaviour that one dislikes or disagrees with. "He has no tolerance" means he does not have the willingness to allow other's mistakes. It means that he can get irritated or angry very easily if somebody makes a mistake. This perfectly describes the subject, "my father", who is a person who gets very angry easily. Hence, this word most appropriately describes the subject, "my father". Hence, option A is correct.
Option B: The word, "impatience" is an abstract noun which means: The tendency to be irritable or restless. "He has no impatience" can be restated as "He has a lot of patience". A person who has lot of patience does not get angry very easily. Hence, this word cannot describe the subject, "my father", who is a person who gets very angry easily. Hence, this option is incorrect.
Option C: The word "solution" is a noun which means: The answer to a problem. It is not an adjective and it cannot describe a person who gets very angry easily. Hence, this option is incorrect.
Option D: The word, "tolerate" is a verb which means: Allow the existence or behaviour or practice something that one dislikes or disagrees with. As tolerate is a verb and the blank has to be filled in by an adjective, this option is incorrect.