Two lines are parallel if they have the same slope
The slope of the line y = 2x + y = 12, is found isolating y, as follows:
2x + y = 12
y = 12 - 2x
this means that the slope is -2
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept
Replacing with m = -2 and the point (5, -6), we get:
-6 = (-2)(5) + b
-6 = -10 + b
-6 + 10 = b
4 = b
Therefore, the equation is:
y = -2x + 4