That's pretty poor quality. Besides the noise, there is also reverberation/echo and distortion on the voice.
You should be able to clean up much of the noise in Audition. But, it's a balancing act between reducing the noise and not affecting the voice too much. With this poor quality, don't expect miracles. Here's the basic procedure. Did you basically follow this?
First load the audio file and display the waveform editor. Here I dragged the bottom of the frame up to display the spectral display also. Zoom into the waveform until you can easily find the space between the words.
noise1.jpg
Open the noise reduction effect (keyboard shortcut ctrl+shift+p). If you haven't sampled the noise yet, you'll get a message to do so like this screen capture. Select one of the spaces between words that is typical of the noise you want to remove and click "capture noise print".
noise2.jpg
After you take the sample, click on "select entire file". It should look something like this:
noise3.jpg
Now you need to play with the settings to find the best noise reduction. The two main sliders to adjust are "reduce noise" and "reduce by". Start with a setting of about 60% and 30db respectively. At the lower left corner there is a preview play button. Click it to hear the audio as you make adjustments of each up and down until you find a setting that reduces noise without drastically altering quality the voice. I also adjusted the "spectral decay rate" in advanced. I thought 25% sounded better. When you are satisfied with the results, click on apply.
For comparison, here's what the waveform/spectral display looked like with the 60/30 setting.
noise4.jpg
And, here's what it looked like with a 100/60 setting:
noise5.jpg
Notice the last one had removed almost all of the noise, but the voice waveform is noticeably different. I thought the 60/30 actually sounded better with less distortion.
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