Press it over the damaged area and turn until you reach the padding then pull out the circular piece and patch as you would a large section.
Replace section of carpet pad.
In either event be prepared to vacuum up a lot of dirt and possible degraded carpet pad.
Using a razor knife cut around the section of padding you are removing so you can pull it away from the rest of the padding.
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If you are only replacing a 6x9 foot area with no seams i would likely just replace the carpet and pad if i could find a usable pattern on roll at lowes or home depot or a remnant at a dealer.
Older carpet in high traffic areas might be more faded.
If carpet tape is not doing the job you can also use carpet glue to hold the patch in position.
Keep in mind that if you plan on replacing the carpet the patch will adhere to the padding making it harder to salvage the pad.