While it seems improbably that two obverse die were clashed, this is what has happened in this case.
The top two pictures show the obverses of each coin. The third picture shows the position of the clash when it occurred. Note that the obverse die has been flipped but not inverted since the clash deals with two obverse dies.
The PUP for this clash on the 1857 Flying eagle cent is on AMERICA. Liberty's left arm cross through the letters of AMERICA, down to the eagles tail.
Of the clashed coins seen for this date, the 1857 Flying eagle cent clashed with the Seated Liberty half dollar seems to be the most common and easiest to detect. Even Flying eagle cent coins that are in grades AG-3 readily show the clash mark.
The overlay image is courtesy of Rick Snow.