First, consider the equation of a line: y=ax+b
Recall: if two lines are parallel, their slopes are equal.
We want to find a line that is parallel to line y=4x, that means the slope of the line that we want to find is 4.
Rewrite the equation of line: y = 4x+b
Since this line contains(4, -6), we can solve for b. Plug the point into y=4x+b, -6=4(4)+b, b=-22
Hence, the equation for the line is y=4x-22