I have a generator with a 3 wire output(nema l6). It is 3000 watts and 120/250v output

I have installed a transfer switch in the house that has a 4 wire input (nema l-14).

Can I use this generator? Can someone explain to me the difference in the wiring between these two connector types.

Thanks

A NEMA 6 receptacle is NOT a 120/240v (125/250) receptacle. That is a straight 240v receptacle and CANNOT be used with a transfer switch at 240v. There is NO neutral present at that receptacle.
Typically a genset that small will not have the required 120/240v NEMA 14 receptacle.