Lucy, who is educated at home, sent in a very clear solution to this question. For the first part she wrote:

You move the top peg to the right by one space. If you cut a square from all four corners, you end up with a quarter of it. In the middle of the square you get four right angles.
 

I think there is at least one other way to get a right-angled triangle. Can you see how?

Lucy continued:

For the second problem you know that the new shape is going to have sides $4  \times  8$ because the sides are multiplied by $2$. One of the sides is already $4$ so you just move the two right pegs $6$ spaces to the right.
 

Very well described solutions Lucy, thank you.

Matthew from Beechwood Park School 
wrote:

Yes:
To make the triangle a right angle triangle in one move you move the highest band to a perpendicular angle to one of the other angles, and to make the rectangle longer you move the two furthest right corners to the furthest right pegs (in line with them).