Yes it is the one with 4 different sand paper pads. I think the longevity of the clear effect comes from reapplying the UV protestant.
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Or $4.00 for a can of Aerogard... And a rag.
Then buy some 3M Clear sheet (has UV filtering in the sheet) and apply over the headlight - will prevent it coming back...
When you're finished the headlight makeover
I use autoglym bumper gel to maintain the finish and is easier to apply
Cheers smally