◯ Eigo o hanasemasu ka ◯ Eigo ga hanasemasu ka × Eigo ga hanashimasu ka hanasemasu ka= Can you speak ? hanashimasu ka= Do you speak? Yes, it's correct. I hope this helps :)

hanaximasu and ga here is wrong. This sentence you read actually means CAN yiu speak English. And hanasemasu=can/be able to hanaximasu. or hanase=can hanasu o means eigo is object and hanasu is a transitive verb while ga has mutiple roles. It may follow an intransitive verb or indicate the noun before it is subject.

If it wasn't already clear, I'll restate what others have said in a different way. I will use demonstrative statements instead of questions. Eigo ga hanasemasu = means to be able to speak English Eigo wo (o) hanashimasu means to speak English, that is, to use English to communicate. For example, when i talk with my friends from Japan, we use English. Ni hon jin no tomodachi to shaberu toki, watashitachi ha (wa) eigo wo (o) hanashimasu. This is what my friend told me. My Japanese isn't perfect, so maybe someone can verify :)

1.Eigo o hanasimasu ka? (えいごをはなしますか？) 2.Eigo ga hanasemasu ka? (えいごがはなせますか？) In japan "Eigo ga hanashimasu ka" is strange sentence. this is "Eigo speaks ..." ,so this sentence is strange. Difference between 1 and 2 is that 2 empasizes the English. 2'sentence seems to emphasize ability a bit more. 2 is better expecting to speak English than 1. My English is bad. I'm sorry＞_＜