Rearranging Tiles

Discrete Mathematics Level pending

This painting is made from 12 different tiles:

If the tiles are all removed and replaced randomly (i.e. they can be rotated and/or moved to a different section of the 4x3 grid) how many different ways are there to rearrange the tiles?

Feel free to include only one significant digit.

Assumption: One arrangement consists of each of the 12 spaces above filled with one tile face up in one of four possible orientations (rotations). No turning tiles upside down.


Image credit: https://www.rods.com

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