Yes, "to assume" is "annehmen", "vermuten", "unterstellen", "voraussetzen".

I would say more like in English "We take it that they have kids?" So take it, or take on, like we take it upon ourselves to think. or Ass u me. or literally We take (it) (up)on (ourselves) that they have children. :-) Definitely an idiom in English.

They are the same verb. The verb gets splitted into two pieces in certain situations. The verb stays one word in sentences with an auxiliary verb.

• Ich kann annehmen, ... (=I can assume) Ich will annehmen, ... (I want to assume)

• But: Ich nehme an, .... (I assume) Ich nahm an, ... (I assumed)

• Ich habe angenommen,... (I have assumed)

Ihnen = 'them' and sie = 'they' or basically, Ihnen = to you (formal singular & plural: You, them) for sie one mostly only knows if it's "she" or "they" by the verb form, ex: Sie ist, oder Sie sind, and if it's formally capitalized in the middle of the sentence meaning formal 'you'. But if not capitalized, look to verb form.

But one way to remember... Sie wissen, sie weiß ihnen. "You (They) know, she knows them." (note: ihnen not Capitalized) oder Sie wissen sie weiß Ihnen. "You know she knows you." Capitalized Ihnen, with/without the comma. (added: I believe the second wissen should be kennen if one means knows (the persons) them, as opposed to knowing their personality, likes and dislikes etc.) Someone pipe in if I'm wrong in this, thanks. Was, wer man Duzen oder Siezen, "ihnen" oder "Ihnen". Wie sowie, alle dich, oder alle sie.

Of course, this is in writing. Speaking it's ambiguous (except that last sentence in German), like the other examples. In most cases ambiguity is only removed with context, and in writing, it appears that lower case is an indicator of informality and so understood as such. But, Capitalized "Ihnen" is generally "You"; and without a capital "them", and this means at the start of the sentence too, and never done without caps at the beginning so choice is limited. If one is speaking formally, or informally, can make a difference too.

With Duo, when ambiguity happens in English and translating, either word is generally accepted. Often, to remove ambiguity, Duo will either leave you with only one choice, picking bubbles, or by partially answering with a word or two that clarifies the choice, or the use of that word at the beginning of the sentence; but even at the beginning Duo usually recognizes when an ambiguity can exist.

Sie kennen is generally understood as formal "You" or "They", and ihnen without caps is generally understood as "them"; it would probably sound strange to say "Ihnen kennen" to say "They know, or You know" but it would probably be understood as "You" plural, again depending on context and Sie kennen works just fine. I generally default this way, as there's no telling what Duo will accept at times.

There's so much ambiguity that I'm sure even Duo forgets one correct answer from time to time. We in English have the same problem between, "You", meaning "you plural", or 'one' formal where an Accusative "you" can be interpreted wrong. "You don't often see that!" "No, I see it all the time!" "I mean, one doesn't often see that." "Yes, I only see it because I work at the dump!" ;-) In English we do at times see people offended when one uses 'you' singular informally. "You can't do that!" only to have the person misunderstand that one meant "That is not how it's done; and instead interpret it as being told they can't do it, or are incapable of doing it. Slightly off track; but I have a gut feeling that being misunderstood because of mixed concepts in a single word happens in a lot of languages, if not all of them.

Wir*

I could be possible that Duo just wanted you to put the word together: Annehmen. Wir annehmen, dass sie Kinder haben. I especially like it with the comma; but I'm no expert. But, we can't forget that Duo generally ignores punctuation, and if it's right with a comma; it may be wrong without one. IOW without the comma it means: ""We assume that you have children" with a comma it means, "We assume that they have children" or so I think. :-) For me, it will be a long time before I get that example again, as I just finished level 4 a couple weeks ago, and level 5 is a ways off.

I tested it with GT (Google Translate) and GT changes the meaning based on comma use. Like I said, I would need to test it with Duo, and if one gets it right the first time, no more opportunities... perhaps.

FWIW you could have edited the previous post you made to correct it, instead of making the correction in a new post. FYI

The better I learn German, the better I am at forcing GT to show me what it can do, right and wrong. :-)