Sometimes I think they do this on purpose. Mi siquiera does not make any sense so even though it doesn't sound correct you should have been able to properly translate to ni siquiera. I know it's frustrating but it's part of the learning process. Try to remember that you aren't just translating words, but phrases.
I would like it online so I could make a note for example "Using ni siquiera" and have it link back to this page. It would be 'searchable' like building our own dictionary based on discussions. Ideally we could link it to an independent dictionary or other spanish website. I do all I can to do everything online. I belong to another group and use Google Drive. Perhaps you can use find in Google Drive, I haven't tried.
One is positive, one is negative. I think the challenge is that in English the phrases are a little different, but if you think of it as "even" and "not even", maybe that will help.
i.e, Even though I was late, I'm here./ I'm late, but at least I'm here. >>> Siguiera estuve tarde, estoy aquí./ Estoy tarde, pero siquera estoy aquí.
vs. I arrived here and I wasn't even late. >>> Llegué aquí y ni siquiera estoy tarde. (I wouldn't be surprised if I misconjugated llegar for the 1st per preterite, but hopefully the illustration makes sense and helps in spite of that.)
Since drink is an irregular verb in English (drink, drank, drunk), with the past tense drank, I'm not clear on the translation with bebieron.
The core of the sentence, is "Ellos bebieron jugo." I would translate this as They drank juice.
When ni siquiera is inserted into the sentence, why does the form of the English move from "They drank" to "They did drink"? This doesn't seem like the same tense to me. Is it the same in Spanish? It seems like it would require another verb, like hiceron. Confused!
My guess would be that your submission wasn't accepted because there isn't a "never" word in the sentence (like "nunca"). And this is one of those places where modern English and Spanish aren't totally compatible, because we don't typically say "they drank not". So instead they want us to use "did not drink".
That's my theory anyway :)