Is it possible to create a 22 stage synchronous counter using multiple 4-bit synchronous counter?
This type of counter can be cascaded to produce an N-bit synchronous counter. Some data sheets for this style of 4 bit counter show how the connections are done. The diagram below is from this datasheet.



Please be aware of the note on the diagram that the maximum clocking rate is reduced by adding additional stages due to the propagation delay of the carry look ahead circuitry in each stage. 

There is an alternate way to hook up the additional stages so that the maximum count frequency is not affected by more stages. See below: