It would be a mount for a 545RFE Chrysler 5 speed auto if I recall correctly. The 2007-2012 3.8 V6 was paired with the 42RLE Chrysler 4 speed auto used in the 3.8 and 2011+ CRD and the 2012+ 3.6 V6 used the Merc W5A580 Merc 5 speed auto.
From what I remember seeing long ago, all 3 transmissions have very different looking cases and from
this picture, the 545RFE transmission mount looks very different to the other 2.
Since the transmission mount is basically two rubber blocks inside a steel frame, I'm guessing the rubber on yours has perished. I've never heard of it being done, probably because it's a $50-$60 part that wasn't worth the effort, but I wonder if it's possible to "rebuild" it by replacing the rubber blocks?