"Can you write this?"
Translation:Вы можете написать это?
«Написа́ть» is the usual perfective: 'to successfully finish writing'.
«Записа́ть» emphasises the fact of creating a written record, written version of something. You don't just finish writing, you create some sort of written record. «Записать» can also mean 'to record' (записа́ть ви́део — to record a video).
- она́ написа́ла стихотворе́ние means 'she wrote a poem' (she is the poet who wrote this poem),
- она́ записа́ла стихотворе́ние means 'she just wrote down the poem'; it doesn't say if she is the poet or not. Maybe she is a poet; maybe she is not a poet — we don't know, this sentence doesn't tells us. It just says that she created a written version of the poem.
It sounds very strange.
«Ты умеешь писать?» 'Can you write?' or «Ты умеешь писать такое?» 'Can you write such [things]?' works, but it doesn’t work with «написать» (because it refers to writing just something once) or with «это» (because it refers to some specific writing).
«*Вы можете писать это?» doesn’t sound well to my ear.
If you wanted to ask about the general ability, you’d use a different verb: «Вы умеете писать?» (and even this doesn’t sound too well if you add «это»; «это» somehow supposes writing a single thing and this doesn’t work too well with a repeated «писать»).