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Look at what happens at the y-intercept (when x is 0):
y = 4*0-6 = -6. How do we shift that point down 3 units? In other words, how do we make y = -9 when x=0?
-9 = 4*0-6+c where c is a constant. ---> -3 = c ---> so we subtract 3 from the constant in this equation.
y = 4x - 6 - 3 = 4x -9
The equation of the line shifted down 3 units is y=4x -9.
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