i've got some emails about my comment and i hope i can clear it up with this post what i meant:
the problem with this "Wir mögen Sie" is, that in Germany you use a respectful personal styling for unfamiliar persons in documents. That means if you would write in a letter "wir mögen Sie" the "Sie" with a capital "S" means you address the "wir mögen (we like ...) directly to this single unfamiliar person, because the "Sie" is directed only for this person alone. But if you write in a letter "wir mögen sie .." the "sie" with a lower case "s" means you address a group of persons.
A quick example like a business email could look like this: "Sehr geehrter Herr XXX, ich möchte Sie gerne sehen ... " (Dear Mr. XXX, i would like to see you ... example for address a unfamiliar person in a honorific way"). On the other hand if you would write "..., ich möchte sie gerne sehen" it would mean you would like to see for example a rock band and not a distinctive person. Around the 1900 if you would have address a persona in the common low case style you would have insulted this person, nowadays they don't take it that seriously but still it shows respect and of course that you know what you are doing!
This form of writing is also used by "Du" e.g. "Magst Du mich?" ("do you like me?" familiar Person like a Friend, who you address by his forename) or when a third person is meant with "Er" e.g. "... Du sagst, Er mag mich ... " ("you said he likes me" talking about a third person with your friend in a letter).
So it is important for non native Germans to see the difference right away in the spelling of personal pronouns, if it is meant as singular, plural or even as honorific. That's why i miss by the translations maybe a short hint like "personal conversation" or "business letter", cause even i as German would translate "We like you" as follows "wir mögen dich/sie" with lower case "s" or "d" and i would get a error cause of wrong spelling ... its just confusing without a hint!
Certain verbs in German require the direct object to be in dative. Danken is one of them but mögen is not.
That's why it's Wir mögen Sie buy Wir danken Ihnen.
be careful you are mixing right now the cases (nominative/genitive/dative/accusative). In short, no you cant. Correct would be ...
unfamiliar single person - "Ich danke Ihnen"
unfamiliar group of persons - "ich danke ihnen"
familiar single person - "ich danke Dir"
familiar group - "ich danke euch"
unfamiliar single person - "Wir mögen Sie"
unfamiliar group of persons - "Wir mögen sie"
familiar single person - "Wir mögen Dich"
familiar group - "Wir mögen euch"
for more help have a look at ...
No, it can t be constructed like that. "You like us" would be "Sie mögen uns". Uns - accusative (and dative as well) case of "wir". So you can say "Sie mögen wir" and still it means the same "We like you" (probably when you want to emphasize, that YOU are the one we like) but with this word order it can be understood also as "We like her" or "We like them" - "Sie" is the first word of sentence, thus we don t know if it is "Sie" or "sie" I hope you understand what I`m trying to say:)
I think you may have clarified something for me there. If you just hear the sentence 'Wir mögen Sie' (i.e you don't know if it's capitalised or not, could it be any of the 3 possibilities i.e. 'We like you (capitalised formal), them (uncapitalised plural) or her (uncapitalised feminine singular accusative)?
i dont know who is handling the German translation from Duolingo, but you guys should maybe consider to explain the German salutation forms before giving anyone a translation task. Cause you mix the formal form of address from Bussiness Letters and such with the normal street conversation and thats really not helping at all! ... i'm native German and i have to think twice