Help on the use of the が particle in this specific example.

I am going through JLABs Anki deck and came across this sentence which translates as “[I] was thinking about what [I] can do myself the whole time.”

自分 に 何 が できる か を ずっと 考えて いた

Why is the first relative clause using those particles instead of being written like this?

自分 が(or わ here maybe) 何 を できる か を ずっと 考えて いた

Having the が particle on 何 makes it seem like the 何 is the subject that is できる, but that doesn’t really make sense to me.

by SoopaTom