can I connect 120/240 split phase washer If I just have 3 phase 220v?
As threephaseEel is pointing out it depends on the configuration. I would hope it is a Wye all 3 phases have the same voltage to ground but with a delta the the B phase is "wild" or 2x the other 2 that's when things go boom. If your voltage is 220 the line to neutral value should be 127V depending on the washer's wiring this may work if code legal in your area and the washer requires 120V.
Almost all lighting in industrial plants are from Wye connected transformers using 1 leg, for example : 480V 3 phase 1 leg to neutral is 277 or 480/1.732. The neutral connection back at the transformer is connected to the ground.  A more common example in light industrial facilities Wye connected also would be 208/120 3 phase the line to neutral here is only 120V  (208/1.732).
In my early days the low voltage 3 phase was 230V this is a bit high for a single leg to ground on a 120V but it was used back then there was not as much digital electronic gear I believe this is the reason 208 3 phase has become the standard now. Verifying the actual voltage and connection type is very important. With all 3 legs to ground measuring the same value it is a Wye connection. Measuring the legs to ground and 1 leg (usually the B phase) is 2X the voltage is a Delta you cannot use the B leg or "wild" leg, but the A &amp; C leg can be used for 120.