In 1942 there were a total of 315,472,329 Mercury dimes produced by three U.S. mints. The Philadelphia mint made over 205 million of the coins, while the Denver mint made 60.7 million dimes and the San Francisco mint 49.3 million dimes in 1942.
The Philadelphia mint did not use a mint mark while the Denver mint used the letter "D" and the San Francisco mint used the letter "S" as their mint mark, so almost two-thirds of the 1942 Mercury dimes did not have any mint mark at all.
If your Mercury dime has a mint mark it will be located on the reverse or Fasces side of the coin, not on the side with the image of Liberty wearing the winged cap. It is located at the bottom just to the left of the pillar and below the branch. Between the word one and the bottom of the branch.
This one has no mint mark so it is from the Philadelphia mint.