。
She seems to know the knack of writing letters.
Literal
She [topic-は] letter [object-を] write knack [object-を] knows [it seems-ようだ].
こつ (knack/trick) refers to the practical skill or technique that makes something easier — knowing the こつ of letter writing means she understands the art of composing effective letters. ~ようだ (it seems/appears) adds the speaker's inference based on observation: she appears to have this skill, but the speaker isn't certain. 知っている is contracted to 知っている in the standard form here.