I got intercept = (3, 0); y-intercept = (0, -4). Am I right?

You have an equation for a line, remember that:

the x intercept is where y = 0 and the y intercept is where x = 0

So set each one to zero in your equation and check your answer:

3x - 4y = -12

for the y intercept x = 0

-4y = -12

y = 3

so... (0,3) is your answer

for the x intercept y = 0

3x = -12

x = -4

and... (-4,0) is your answer

it looks like you've confused your answers.

Remember that if the line intercepts the x axis it's because the value of y at that point is zero.

And if the line intercepts the y axis its because the value of x at that point equals zero.

On the y axis, there is no value for x.

On the x axis there is no value for y.

When you get to 3D:

on the x axis there is no value for y and z

on the y axis there is no value for x and z

on the z axis there is no value for x and y

This would be much easier to demonstrate with a drawing but I have to operate within the constraints of the website. Anyways, I hope I helped you out.