Write an equation of the line passing through point P (2,3) that is perpendicular to the time y-4=-2(x+3)

Perpendicular lines have a slope that is equal to the negative inverse.
Slope is m=-2 so the new slope would be m=-(-1/2)=+1/2

Then use point slope form y-y1=m(x-x1) to get

y-2=1/2(x-3)

y=1/2x+1/2