There is no handy frequency multiplier block like you show in your diagram.
Probably the best way to do this is to convert the incoming AC power to DC, then chop that up to drive the work coil. If the work coil is fully insulated, then it doesn't need to be isolated, which saves having to use a transformer and the associated cost, size, and efficiency loss. If you do need isolation, then have the chopper drive the transformer.
One wrinkle you shouldn't ignore at the power levels you are probably intending is the power factor this unit presents to the AC line. The AC to DC conversion should include power factor correction. This is required in some jurisdictions above a certain power level. In the US, it's not so much a requirement as that large customers get billed more for low power factors. In the EU, there are outright regulations for minimum power factor depending on power draw.
Any competent power supply you get at such power levels will do power factor correction anyway. That industry is highly competitive, and you won't be able to beat buying a off the shelf supply unless you have very unusual requirements or your volumes are very high. There is a lot of engineering that goes into a good AC to DC power supply, and it's somewhat of a specialty of its own. It often doesn't make sense to design your own power supply.
You say you want the output to be a specific frequency. That doesn't change anything. You control the oscillator or chopper that makes this frequency from DC. You apparently want to exploit resonance, which is a reasonable idea. So make sure that the system resonates at a reasonable frequency, and that the oscillator is tuned to that frequency.
None of this has anything to do with the 60 Hz power frequency. That's way too low for resonance with reasonable size parts. Using individual 60 Hz cycles to "ping" the resonant circuit at 60 or 120 Hz makes no sense. The Q would have to be very high to sustain 24 kHz ringing for 200 cycles between 120 Hz pings, which isn't practical when you want to take significant power from it. You also would have to artificially create the 24 kHz content to ring the resonant circuit with anyway. You might as well do this every cycle with a 24 kHz oscillator, then once or twice each power line cycle. That concept makes no sense.