At what two azimuths does the celestial equator intercept the horizon?
An azimuth is a measurement in a spherical system, like our sky. For purposes of this question, you can think of azimuth as corresponding to the degrees on a compass, with the "0" point being North. If you turned around and faced South, that azimuth would be 180 degrees. This would put East at 90 degrees and West at 270.
The celestial equator is an imaginary line in the sky; it doesn't actually describe a real feature of the universe. Rather, it's a way of making sense of our perspective, looking out from the surface of the earth. The celestial equator is really just a projection of the earth's equator, dividing the celestial sphere in half.
As the earth goes through its seasons, the height that the celestial equator reaches in the sky will change, but the point at which the line intercepts the horizons will always remain the same. This point is directly east and west, anywhere on the earth. These two azimuth are 90 degrees and 270 degrees.