My fiancee got a kidney stone of 6mm in size according to the ultrasound, is it possible to pass it without surgery?

Ureteral stone. The size of the stone does not correlate well to the intensity of the pain. The nearly unbearable pain of "ureteral colic" is from spasm of the muscular ureter. Although likely to pass on its own within a few days, a 3mm stone sometimes will get stuck and fail to progress. A 6mm stone, less likely usually after 5 days, i recommend having the stone extracted with a ureteroscope as an outpatient.
It is possible. But issues of duration of obstruction, ureter blockage may influence. I've had 16 and painfully passed all without surgery. Always check with your urologist for benefits and risk, and if in doubt seek a second opinion.