For the second one, I think the best way is to find something that's unique in the unfolded piece. I grouped them up into 4 main triangles. One thing I noticed on the very right triangle is that it has a shaded triangle touching another shaded triangle. And looking at the inside area, there's no other way for to get a 2-shaded half triangles. This allows us orient the object in the answers.
For answer A, that very right triangle piece in the unfolded image must be the bottom triangle that is not shown. Folding it will show a mismatch. The shade on the very left of answer A shouldn't be there I think.
Doing something similar for B, we see that 2-shaded touching triangle this time, so we instantly know our orientation. We can immediately eliminate this answer.
C, again, same thing. This mayb be the answer. I would skip to D to see if it could be eliminated.
Everything looks like it matches. I'm just questioning whether or not this view is possible. It does look possible, everything is just hidden.
Going back to C, I don't think there should be a shade at the very bottom of answer C.
Actually looking back at it now, the 1 of the 4 main triangle that has the 2-shaded touching triangles have their triangles in the incorrect spots. The white piece should be at the up-left position.
Is the answer D?