No, you can not export AVCHD video from Premiere Elements.
You can export MP4, which is compressed with H.264 like AVCHD -- it just isn't true AVCHD.
You can also export MTS, which is the hi-def format used by HDV camcorders.
Welcome to the forum.
As Steve says, you cannot Export/Share precisely to AVCHD. What is your intended delivery scheme - BD, DVD-Video, streaming video on a Web site, playback on a computer from a DVD-Data disc? That will give us some guidance on directing you with the best format/CODEC.