In order to find the ordered pair of this vertex after the translation, we just need to calculate the effects of the translation.
A translation of 6 units to the right means we need to add 6 units to the x-coordinate.
A translation of 10 units up means we need to add 10 units to the y-coordinate.
So if the original vertex is (4, 1), the new coordinates will be:

So the ordered pair of the vertex will be (10, 11).