Paul doubles the amount that he ate on the second day, so eats 2 x 2 = <<2*2=4>>4 sandwiches.
For the third day, he doubles the number of sandwiches he ate on the second day, so eats 2 x 2 x 2 = <<2*2*2=8>>8 sandwiches.
To get the total amount of sandwiches he ate over three days it's necessary to add up the amount he ate each day: 2 + 4 + 8 = <<2+4+8=14>>14 sandwiches
Since he eats 14 sandwiches every 3 days, then in 6 days he would eat 14 x 2 = <<14*2=28>>28 sandwiches in total.
#### 28