My best friend likes watching movies and playing basketball.
Parallel structure is when the items in a list have the same grammatical structure. In the correct option, both of the items in the list are written as gerunds. Gerunds are verbs ending in /ing/ that are used as nouns. Here the gerund form is used to explain which activities the best friend likes. The other options do not have the same grammatical structure. For example the last option has the gerund from of watch but the infinitive form of play. They are not the same.