Determine the reactions at the supports?

Total of the distributed load = 75 × 8 = 600 N:

This is shared equally amongst A and B so the respective reactions are each 300 N.

In this case "by symmetry" is a good enough reason for the equality of the load sharing.

Then there's the moment of 800 N.m applied at B:

This is reacted by a force at A which produces an equal and opposite moment about B and is therefore 800/8 = 100 N

So in total:

the reaction at A = 300-100 = 200 N and

the reaction at B = 300 N.