Can I move a block (text or image) from one section to another section on same page?

Can I move a block (text or image) from one section to another section on same page? 

So far I can't seem to do it. I am trying to break up my page in to a lot more sections, rather than 1 really long section with text and image blocks. But, since I can't move or drag blocks from one section to another this is taking forever 😞

Thanks.