Final answer:
The verb 'begin' should be changed to 'begun'.
Step-by-step explanation:
The correct form of the verb 'begin' in the given sentence would be 'begun'.
So the sentence would change to: 'He has begun living here six months ago.'
'Begun' is the past participle form of 'begin', and we use the present perfect tense ('has begun') to indicate an action that started in the past and is still ongoing.