The given point (0, -4) lies in quadrant III. Let's understand why.

Quadrants on a Cartesian plane:
A Cartesian plane is a two-dimensional coordinate system that consists of two perpendicular lines called the x-axis and the y-axis. The point of intersection of these two lines is called the origin. The Cartesian plane is divided into four quadrants, numbered from I to IV, in a counterclockwise direction.

Explanation:
1. Understanding the coordinates:
- The given point (0, -4) has an x-coordinate of 0, which means it lies on the y-axis.
- The y-coordinate is -4, indicating that the point is 4 units below the origin.

2. Analyzing the x-coordinate:
- Since the x-coordinate is 0, the point lies on the y-axis.
- The y-axis is the line perpendicular to the x-axis, passing through the origin. It divides the Cartesian plane into two halves: the positive y-direction and the negative y-direction.

3. Analyzing the y-coordinate:
- The y-coordinate is -4, which means the point is 4 units below the origin.
- In the Cartesian plane, a positive y-coordinate represents a point above the x-axis, while a negative y-coordinate represents a point below the x-axis.

4. Determining the quadrant:
- Based on the x-coordinate being 0, the point lies on the y-axis.
- Since the y-coordinate is -4 (negative), the point lies below the x-axis.
- Combining the above two observations, we can conclude that the point (0, -4) lies in the negative direction of the y-axis, which corresponds to quadrant III.

Therefore, the correct answer is option 'C' - the point (0, -4) lies in the negative direction of the y-axis.