Translation:From that entrance, please.
In Japanese I kept asking people questions expecting a response, and nobody answered. Then I learned to use (postpositional rather than prepositional) particles instead, no verb at all, and the difference was night-and-day. I've come to think they serve the function of eliciting responses that verbs do in the imperative and interrogative questions in English . . .
E.g. rather than, "質問はありますか？" "質問は？（どうぞ。）"
入 means "enter" and 口 means "mouth" or "opening". If you're abbreviating it for a sign, basically all the meaning is there just writing the kanji on their own.
English signage is full of common abbreviations which leave out all sorts of letters. It wouldn't be appropriate to write "St" or "Hwy" every time you meant "Street" or "Highway", but when you see it in a reasonable context, it's obvious what's meant. In a way, it's even nicer with kanji than English can manage, because so much of the meaning is preserved, even if you didn't know the original word.
anyone having trouble with this sentence here is a small breakdown
そちら that way, similar to how そこ means "something that's near the listener and away from the speaker", そちら means "that way" implying that the listener is closer to that. そちら is part of keigo or polite Japanese speech, you will often see customer service using this word.
そちらの入り口 pretty self-explanatory, "the entrance which is that way" would be a better literal translation.
から it's a particle meaning "from", it can be used as a limit to counting or as an originator, in this case, is limiting a direction so it means "from" as in "from the entrance which is that way"
どうぞ is something along the lines of "by all means", this is also part of polite speech and something customer service use often, the difference in this goes deep into the uchi-soto concept of Japanese culture, in short, customer service should always treat the customer with utmost respect while the customer is expected to be polite but not overly polite. For example, you would use ください or お願いします to ask for things and they would use どうぞ to give them to you.
So from the context, we can assume you are probably entering a location where there is customer service, maybe a hotel or something similar, the doorman is telling you "from the entrance which is that way, by all means", maybe because the door you are trying is blocked or closed, this sentence can be better translated as "from the entrance which is that way, please" which is something that sounds natural in English speaking countries from their customer service.
Does anyone even know what the purpose of the sentence is supposed to be? Only half reasonable scenario I can come up with if I ask someone about directions to a place in a large park or on a campus via phone or other means where it might not be clear from where I'll approach the place. But I'm not even certain if I'm correctly interpreting the sentence.
So from what I've noticed, here in Japan they have a lot of people whose job is direct traffic or guide people around. So maybe it could be used in that kind of situation. Or maybe it's just to show use one way you can use どぞう because I've noticed quite a few different ways that I would've never thought of.
Maybe, but not here. In a way it's the same idea, so if you were an independent translator, you could translate it as "please enter there", but Duolingo wants to make sure you know the individual words. I.e. for the moment, you'll have to stick to (nearly) literal translations.