Well with this we use process of elimination.
My brother will provide us up for a few nights.
That set of words doesn't make sense so we can cross out A.
My brother will provide us in for a few nights.
This set of words makes a little more sense so we won't be fully crossing out B.
My brother will put us up for a few nights.
Again, this set of words doesn't make sense so C is eliminated.
My brother will put us in for a few nights.
That set of words makes sense.
So now, it is between B and D.
Now it's up to you to decide which fits better.
Hope this helps!