Translation:We are going to demonstrate that we can cook.
I believe that you could also translate this as 'We are going to demonstrate that we are able to cook'.
The sense of the sentence would be the same, but there is a more literal way to say that in Spanish: We are going to demonstrate that we are able to cook = Nosotras vamos a demostrar que somos capaces de cocinar.
It would require "lo" before the "que" to mean "what". Vamos a demostrar lo que podemos cocinar.
If DL is not being picky about "we will demonstrate = demostraremos / we are going to demonstrate = vamos a demostrar", it is probably because you wrote "what" instead of "that", "what" is "qué" and "that" is "que" ;]
Sorry it's not about the accent. Question words like cuándo, qué, and dónde use accents when they're used as a question, otherwise the accent is absent. It's actually about the missing direct object "lo" which together with "que" as "lo que" should mean "what" as in "this is what I do" (esto es
lo que hago).
Maybe I'm over-thinking this, but should Saber rather than Poder be used in this context? As far as my knowledge stretches: Poder shows that someone can do something in the sense that they are available to do it by having time or materials Saber is used to demonstrate that they know how to do something by possessing the relevant skills.
I think in this case, both have the same meaning and so "saber" would be alright too. I think DL prefers the "know how to..." structure to for "saber" in this context, though!
misheard 'nosotros' for 'nosotras' and got it wrong. Typing 'nosotros' hear has no bearing on the grammar or syntax of the sentence so this should be overlooked.
We are here to learn Spanish not to test our hearing.