The line x - y + 6 = 0 is the right bisector of the segment [PQ]. We are given that P is the point (4, 3), and we need to find the coordinates of point Q.

To solve this problem, let's first understand what a right bisector is. A right bisector is a line that divides a line segment into two equal parts at a right angle.

The equation x - y + 6 = 0 can be rearranged to y = x + 6, which is in the form y = mx + c, where m is the slope of the line. Comparing this equation with the general form, we can see that the slope of this line is 1.

Now, let's find the midpoint of the line segment [PQ]. The midpoint formula is given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the coordinates of P into the formula, we get:

Midpoint = ((4 + x2)/2, (3 + y2)/2)

Since the line x - y + 6 = 0 is the right bisector, the midpoint lies on this line. Therefore, we can substitute the coordinates of the midpoint into the equation of the line to find x2 and y2.

(x2 + 6) = (4 + x2)/2

Simplifying this equation, we get:

2(x2 + 6) = 4 + x2
2x2 + 12 = 4 + x2
x2 = -8

Substituting the value of x2 back into the equation of the line, we get:

y2 = -8 + 6
y2 = -2

Therefore, the coordinates of point Q are (-8, -2).

Now, let's check which option is correct.

Option (a) (4, 4): The y-coordinate is not -2, so this is not the correct answer.
Option (b) (3, 4): The y-coordinate is not -2, so this is not the correct answer.
Option (c) (3, 3): The y-coordinate is not -2, so this is not the correct answer.
Option (d) (3, 2): The coordinates match, so this is the correct answer.

Therefore, the correct answer is option (d) (3, 2).

Answer it