wondering the same.

Bieten supposedly means to offer something, whereas anbieten supposedly means to offer something TO SOMEONE. That's why this sentence confuses me, since it seems to be offering something to someone. I added "an" to the end of the sentence and was marked correct as well, though.

It depends on the 'case' and who you're talking to. German has many ways of saying "you".

Nominative case:
du - talking to one person with whom you're familiar
ihr - talking to more than one person with whom you're familiar
Sie - talking to any number of people formally

du liest
ihr lest
Sie lesen
= "you read"

Accusative case:
dich - one person, familiar
euch - multiple people, familiar
Sie - any number of people, formal (note: same as nominative)

ich sehe dich
ich sehe euch
ich sehe Sie
= "I see you"

Dative case:
dir - one person, familiar
euch - multiple people, familiar (note: same as accusative)
Ihnen - any number of people, formal

ich gebe dir einen Apfel
ich gebe euch einen Apfel
ich gebe Ihnen einen Apfel
= "I give an apple to you"

Such tables are also on Wikipedia, for example.

In the specific example of this sentence from Duolingo, we need dative case because the verb "to offer" has both an accusative (direct) object (what are we offering? 'more') and a dative (indirect) object (whom are we offering it to? 'you'). So, any of the dative options would work here.

Ich biete Ihnen mehr an. Ihnen is the dative case.