How to get 460.8KHz from 1.8432Mhz oscillator using counters?
You could do it with your SN74LS393 counter chip by using the correct output but you cannot simply connect the crystal like that.  You need to turn the output of the crystal into a digital pulse.

You can do this in any number of ways but the most simple is a "Pierce Oscillator":



U1 is an inverter, something like a 74HC04 or you can find tiny SMD parts in SOT/SC-70 cases with a single inverter.  C1 and C2 should be chosen according to the capacitive load your crystal expects, check the datasheet.  R1 is a feedback resistor, you could start with a high value and work downwards until you find it is stable.

Another common way to do this is using D flip-flops, which is essentially how the internals of your counter chip will be working.  The Wikipedia page on frequency dividers illustrates a divide-by-four counter nicely:

 

I have previously done this using 74HCT74 ICs.