To gain access to this front, you must clear a path through the alley that is between the bakery sign on the left and the Little Italy sign on the right. Shoot the explosive barrels and the wooden crates to get through. Go down the alley and kill the Tattaglias at the end of it. Then turn left, find the stairs, and go down them. Crouch down, go through the doorway, and use the couch for cover to kill the enemy in that room.
Proceed carefully to the next room, taking cover wherever you can and killing the enemies. Then turn left, go up the stairs, and turn left again, killing the Tattaglias you find there. In the back of that room, you will find the hidden moneybags.
Now turn around and go into the next room, passing the staircase on your right. Kill the Tattaglia there, plant the bomb, and get the hell out of the building as fast as you can, exiting the same way you came in. If you don't make it out alive, however, you will still get credit for bombing the front.