Answer
Infinitely many.
Work Step by Step
Since points B, C, and D are collinear, there is an infinite amount of planes that contain these three points. To help you imagine this, take a piece of paper and fold it in half. Keeping one half steady, rotate the other half around the fold creating a 45 degree angle, a 90 degree angle, a 135 degree angle, etc. How many angles can you create with the two halves (using the fold as the vertex)? Now imagine that each half of the piece of paper is a plane and the fold is the line containing the points B, C, and D. As you move one half of the paper (plane number one) around the fold (the line) and the other half of the paper (the second plane), consider an infinite number of planes intersecting at line BD.
