Qimage should be autorotating the images to best fit onto the paper. It does not really care about if the images are portrait or landscape since you are going to be cutting them out.  If you insist in a certain orientation you can right click on the image (on the right side pane) and select Set Print Rotation (Degrees) and choose the same as thumbnail on the fly out menu.

I realize these aren't 6 x 4 size prints, but obviously, you made a size typo, so try this:
vertical page set in Qimage.
Go to Custom, and 3rd item from top, Enter number of prints per page. Insert 4 for columns, and six for rows.
That gives you 24 prints to that page.
Now click the padlock to locked as Terry said, and insert your 20 horizontal images.
Make sure crop scissors is on.
The last 4 images to be inserted would be your 4 images that you want to stay vertical. Now insert those.
You have 24 prints on that page the way you asked for it, except they are not 6 x 4 size.

Maybe something above will help??
Fred

So did I Terry. I am still not sure which way is right. 4 x 6 print size, or 4 columns and six rows.
We will have to hear from Mogur2 or 3.
 

So that is what that little padlock is for.  Well that would have saved me a steps in the past.