Based on the sequence of transformations, the coordinates of P" are (-1, 6).
In Mathematics and Geometry, a reflection over the y-axis or the line y = 0 is represented by this transformation rule (x, y) → (-x', y').
By applying a reflection over the y-axis to the coordinates of point P (1, 4), we have the following coordinates of its image;
(x, y) → (-x', y')
P (1, 4) → P' (-1, 4)
Next, we would apply a translation 2 units up to the new point based on the given transformation rule, in order to determine the coordinates of its image as follows;
(x, y) → (x', y' + 2)
P (-1, 4) → (-1, 4 + 2) = P" (-1, 6)