[Delta Whiskey]

In Elements:

Open your Base image. On the right hand side toolbar you will see it listed as a locked layer (padlock symbol),
right-click and select 'Duplicate Layer', give it a useful name.

Left-click the new Layer to select it then:

Use the 'Quick Selection Tool' to pick out the bits you want to get rid of, then right-click inside that area
and 'Select Inverse' then right-click again and choose 'Layer via Copy'. This will cut out the bit you don't want
and put the rest in a new layer with the missing bit transparent ready for the new image to be inserted.

Open the new image, it will cover the original image, use the window tool to hide it (_)

Check that the layer you created is highlighted, then drag and drop the new image from the Project Bin onto it.
Size and change the new image to suit what you want to do. You can move the image in front of/behind the Base image
using the Layers Panel, Left-Click the layer you want to move and drag it up or down in the Layer Panel.

If you want to save the separate layers as one file, use 'Save as Photoshop PSD, PDD'

Once you're happy with your finished image use Shift-Control-E to flatten the layers into one image for saving as a .jpg.