y=x/(x-2)=[(x-2)+2]/(x-2)=1+2/(x-2)
∵4≤x≤6,∴2≤x-2≤4,∴1/4≤1/(x-2)≤1/2
∴1/2≤2/(x-2)≤1,∴3/2≤1+2/(x-2)≤2
即3/2≤y≤2,∴最大值为2,最小值为3/2