Only four pairs that satisfy the condition are: (0,0), (1,1), (2,2), (3,3).
Now the relation can include or leave each of these 4 pairs. Hence 2^4 ways.
For all other 12 possible pairs, the relation must leave them. Hence 1 way.
So no of relations = 2^4 × 1 = 16.
Note that the empty relation is also valid. In that case the condition is vacuously valid.