eslHQ - ing forms

Yes, grammatically it's possible. Here you have a preposition (without), which means that the following verb must be in the -ing form. But that verb (finish), is also followed by a verb in the -ing form, and so they chain up. This can also happen in three verb sequences, where the first and second verbs are both followed by another verb in the -ing form. For example : The doctor recommended stopping smoking. / They advised continuing investigating. However, it often sounds a bit clumsy, and people would normally, I think, switch to an alternative structure for the one or other verb to avoid it : The doctor recommended that he stopped smoking./ They advised continuing to investigate. However, in your example it's not possible - there is no alternative structure as both the preposition and finish only take the -ing form. To avoid it you would have to rephrase the sentence completely : They started to answer without reading the question through to the end.