The answer seems to only capitalise Большой but left the t in театр as small cap (though it accepts my t in Театр in uppercase). We in England call it Bol'shoy (or Bolshoii) Theatre, with the T captalised. Is the Russian equivalent not required to captalise the t generally?
Generally, we only capitalise the first letter of names of different organisations. However, the name might include other capitalised elements, and then these are written with a capital letter. For example: «Национа́льный академи́ческий теа́тр и́мени Я́нки Купа́лы» 'Janka Kupała national academic theatre'. Since Janka Kupała is a name, we capitalise it even though it's not the first word.
This quickly gets ugly when state institutions and officials are involved, because there's often a reason to capitalise every word. Things like «Фонд Президе́нта Респу́блики Белару́сь Алекса́ндра Григо́рьевича Лукаше́нко» 'Belarusian President Alaxandr Ryhoravič Łukašenka's fund' look really ugly. «Президе́нт Респу́блики Белару́сь» is capitalised because it's an official position, «Респу́блика Белару́сь» is capitalised because it's a name of the state, «Белару́сь» is capitalised because it's a place-name, and «Алекса́ндр Григо́рьевич Лукаше́нко» is capitalised because it's a name of the person. And such names are not that uncommon! :x
In English the determiner "the" is usually removed if we are saying the name of a specific place. So if this Russian sentence is referring to a place called Bolshoi that is a theater, it would probably translate to "Where is Bolshoi Theater?". Using "the" is also acceptable, but less common.