Depending on your local electrical code, if you need a grounded (earthed) system, you can use a 400V-Delta to 208/120V WYE transformer to feed a variable frequency drive (VFD), and then set it a 60Hz to supply 208V 60Hz to the motor. Although I do not normally recommend it, if it is appropriate for you to run the system ungrounded (unearthed), then you can feed the VFD with through a 400V-Delta to 230V-Delta transformer and then supply the motor with 230V 60Hz power from the VFD. (As with most North American motors in that voltage class, yours appears to be rated for 230V or 208V operation, although it will probably pull about 8% more current when it is operating on 208V.) There will be no special programming for the VFD, and the motor will operate as designed although it will may run a bit hotter due to the harmonics produced by the VFD.
You can use a VFD to reduce the supply voltage to a motor, because this is a standard VFD function when a motor is running below rated frequency (constant V/f ratio). My concern about the harmonics comes from the fact that you are basically using the front end of the VFD as a switching power supply in much the same way that "solid state" computer power supplies step down the voltage and rectify it in computers and these supplies are notorious for producing harmonics because they do so much chopping of the incoming waveform to reduce the DC voltage to the desired level. For that reason, my preference is to use a transformer to correct the voltage level and then use the VFD to correct the frequency. However, if the harmonic currents drawn by the VFD are low in relation to the size of the power system, going without a transformer would be an acceptable option.
If you feed a VFD with 230Y400V 50Hz, and program the drive for 230V 60 Hz, you will get 137Y230V. This would probably work but I wouldn't recommend it except for smaller motors. By feeding 400V into the VFD to run a 230V motor, I suspect that you would get a lot more harmonics in your supply current and in your output signal as the drive does more "chopping" of the incoming wave form to control its DC bus and output voltages. My preference is to supply the drive with a voltage that matches the motor voltage to minimize the harmonics, you also can go for a GoHz frequency converter to convert 230/400v 50Hz to 120/208v 60Hz at a time, but it will cost more.