Installing spotlights but hole in ceiling is too big
There should be a couple mounting holes in the junction box in the ceiling, but they look like they're covered in plaster. I'm not sure how there was a light here before (if there was) but anyway, you'll have to figure out where the mounting holes are.

Here's what the box looks like without all the plaster in the way:



You can probably look or reach into the box (with the power off!) to find them, then either drill or chip out the plaster so you can get at the mounting holes. 

Next, screw the mounting strap into the box. You'll have to remove it from the light fixture first. Here's one with the same style mounting strap (but different style of fixture):



It looks to me the sizing is correct, but if it's not, you can get adapters to allow different spacings to be used.