The reporters eagerly ............ the speech made by Obama

The phrase “took down” is often used to mean making a written record of something spoken, like a speech. Therefore, Option D is the correct answer. 

The other options do not fit in this context.

Option A: “Took up” usually means to begin doing or learning something.

Option B: “Took on” typically means to accept a job or responsibility.

Option C: “Took off” generally means to leave a place quickly or to become successful quickly.

Therefore, “took down” is the most appropriate choice here. The reporters eagerly took down (recorded) the speech made by Obama.