Translation:Please speak English.
で in this kind of usage, as in right after a phrase like this, means "by way of, by means of, via, using, through" and possibly a few other English prepositions and prepositional phrases. The best translation for this sentence, though, is "In English, please" - because English is weird. If it helps, you can prefer "Using English, please".
Japanese people will be able to figure out what you probably meant, and are too polite (and scared of English speakers) to try to correct you.
There are actually many ways to politely ask someone to speak English. In no particular order:
- 英語でおねがいします is a polite request (lit. "[Speak] using English, I humbly wish")
- 英語で話してください is a polite command (lit. Using English, speak [for me])
- 英語で話しましょう is a polite suggestion (lit. Using English, let's speak)
- 英語で話してもいいですか？ is a polite request for permission (lit. Is it ok, even if I speak using English?)
- 英語で話してもらってもいいですか？ is a polite request for action (lit. Is it ok, even if I have you speak using English?)
- 英語は話せますか？is a question of ability, which in the right contexts can heavily imply your desire for the other party to speak English without explicitly asking them to (lit. Are you able to speak using English?)
It's not necessarily grammatical incorrect, but it does sound very strange and has a very different meaning (something like "English, by stories please").
英語は話してください is also not incorrect, but using を or で instead of は sounds much more natural to me (not a native Japanese speaker).
They are not at all interchangeable; で and を are particles with very distinct grammatical roles.
In this case, で means "by means of" or "using", though it has a few different roles which depend on the context it's used in. So, the sentence here literally means "by means of (=で) English (=英語), I do (=します) request (おねがい)", which in more normal English means something like "In English, please".
The suggested answer for this exercise is "Please speak English" but the verb is only implied; "Please write in English" or "Please sing in English" are/should be equally valid translations.
On the other hand, を is (99% of the time) the "direct object" particle , meaning it indicates what the verb is acting on. So, the sentence 英語をおねがいします would mean something like you are requesting the entity known as the English language itself.
With enough context clues, you could argue that the requested "object" is implying the English language version of something, but I would say that this is an incredibly uncommon and unnatural way to do so and it should still be considered incorrect.
That's pretty much it.
The first two kanji are 'English Language' (I think literally 'English' and 'Language'), and the rest is usually translated as 'please' (I believe the literal translation is closer to 'do me the favour of...' or something along those lines)
There is no actual Japanese for 'speak' in there, but 'Speak English, please' is probably the closest translation of the intent, rather than the actual words...