Crikey!! The new artist didnt hold back on loud design!
Removing new paint from old is a real issue and any success will largely depend on what condition the original artwork is in underneath. The biggest saving grace with a repaint is that the "artist" rarely prepares the surface before repainting - its just slapped on.
 acrylic is tough to get off - i hate the stuff. Enamel is easier. Now hopefully - the original cabinet was not cleaned or rubbed back - if it was then i dont give it much hope.
 But best results ive got is to find a spot where the new paint has a chip or similar taken out of it and to use a razors edge paint stripper - its possible to lie it so flat that it actually glides between the 2 layers of paint. If the new paint is enamel then sometimes you can almost pull it off in sheets as it just peels away. Other parts you can chip away at it and it comes off in flakes.
its a long and laborious job and the kind of job you walk away from several times then go back to.

Good luck mate! I hope for your sake that the original abinet was still in relative good shape