For some reason, sometimes you cannot select images within a Microsoft Word document.
This has baffled me on an off for some time - and I still do not know the reason why it behaves like this.
Today I stumbled across a very simple (and maybe obvious to some) solution... right-click on the image (instead of trying to left-click to select it). This causes the image to be selected and pop's up the context (right-click) menu. Just press the Esc (escape) key to close the context menu, and the image remains selected.