"In the evening, he is going to be in Moscow."
Translation:Вечером он будет в Москве.
In this case it would be grammatically correct, but the emphasis would shift. By default, a new/essential bit of information is conveyed by the last word of a Russian sentence. Hence "Вечером он будет в Москве" tells you where he will be in in the evening, while "Он будет в Москве вечером" tells you when he is going to be in Moscow.
This rule is not 100% strict though and can be easily overridden by intonation in actual speech, but for a written sentence that would be the natural interpretation.
In any case, both translations should be accepted in this exercise.
You translation is grammatically incorrect. Preposition "в" (as well as "на") takes the accusative case to indicate direction and prepositional to indicate a location. The verb "собираться" by itself simply states the intention, and hence cannot be used with a description of a location without another verb (e.g. "быть" - "to be").
You could say "Вечером, он собирается в Москву (accusative)", which would correspond to "In the evening, he is going to head to/for Moscow". While grammatically correct, this would not imply that he will actually arrive there in the evening, it's a statement of when he is planning to depart for Moscow.
I think (I'm still learning, myself) that there are several things that would make your phrase less than ideal.
I think yours comes across something like: In the evening he goes [by foot] in Moscow
Declension of "Moscow" - The Duo translation is emphasizing location (he will be in Moscow) so it's using prepositional (москве), your sentence is emphasizing the direction (he's going to Moscow) so you need Moscow in accusative: Вечером, он идет в москву (In the evening he goes [by foot] to Moscow)
Verb choice - Moscow is pretty big and he's not there now so, while possible, it's unlikely he would walk there. Идти (Идет) implies walking, if you wanted to say "go in a vehicle" you'd want to use Ехать (едет). Вечером, он едет в москву (In the evening, he goes [by vehicle] to Moscow)
Verb tense - We're talking future tense here and Идти (идет)/Ехать(едет) is present tense. Technically I think будет ехать will work but (and note, I'm terrible with aspect) I wonder if the perfective поехать(поедет) might be better: Вечером, он поедет в москву (In the evening, he will go to Moscow)
To add to what an_alias has already pointed out:
How does your sentence account for "to be" in the English sentence?
Also, to elaborate on his/her second point, you could use the verb "идти" (not in this translation, but in general), but you would have to use a correct case and preposition. Specifically,
Идти в Москву (accusative) - to go to Moscow by foot. (Probably OK if you talk about medieval Moscow, but hardly relevant nowadays.)
Идти по Москве (dative, as required by preposition "по") - to walk in Moscow (location, not direction).