Question 827233
y=4x+6 
-15x+3y=-45

The slope of y=4x+6 is 4.  Notice that the form is y = mx + b where m is slope.

To find the slope of -15x+3y=-45 , solve for y
-15x+3y=-45
add 15x to each side
 3y = 15x -45
divide each side by 3
  y = 5x - 15
The slope of this equation is 5 which does not match the slope of the first 
equation, since the slope of the first equation is 4.
Since the slopes are not the same, the lines are not parallel.