Learn Icelandic: Ég veit ekki hvort gjöfin er frá þeim báðum. - I do not know whether the gift is from both of them.

The word báðir (both) changes depending on its grammatical case. Here, it comes after the preposition frá (from), which always forces the words that follow it into the dative case. The dative form of 'both' is báðum, and handily, this form is exactly the same for masculine, feminine, and neuter!

Why do we need the word 'þeim' before 'báðum'?

In English, we usually say 'both of them'. In Icelandic, the structure is literally 'them both'. You pair the personal pronoun þeim (the dative form of 'they') directly with báðum. They must match in case, which is why both are in the dative here, triggered by the preposition frá.

I often confuse 'hvort' and 'ef' for the English word 'if'. Why must we use 'hvort' in this sentence?

You use hvort when you mean 'whether' — usually when there is an implied choice or a yes/no question involved (I do not know whether it is from them or not). You use ef for conditional statements, like 'If it rains, I will stay inside.'

What gender is 'gjöfin' (the gift)?

It is a feminine word. The base noun is gjöf (a gift), and the -in attached to the end is the feminine singular definite article ('the').