When a verb is followed by another verb, the second verb must be either an infinitive with 'to' such as 'to do', 'to make', 'to go' etc. or an -ing form such as 'doing', 'making', 'going'. In this episode of The Flatmates, the police officer says 'Would you mind answering a few questions...?' The form of the second verb depends on the first verb, and/or the speaker's intended meaning.
Some of the rules about verb + verb-ing are given here.