We have collected a 43 event sample of the decay K(L)-->e(+)e(-)mu(+)mu(-) with negligible backgrounds and measured its branching ratio to be (2.62+/-0.40+/-0.17)x10(-9). We see no evidence for CP violation in this decay. In addition, we set the 90% confidence upper limit on the combined branching ratios for the lepton flavor violating decays K(L)-->e(+/-)e(+/-)mu(-/+)mu(-/+) at B(K(L)-->e(+/-)e(+/-)mu(-/+)mu(-/+))< or =1.23x10(-10), assuming a uniform phase space distribution.