vijay,i dun think 6 is the correct answer as it is askign for minimum,,i think if we remove only 3 edges then also it will be disconnected...
if we have to make a graph as disconnected,take a node with the minimum degree and remove all its incoming edges..
for a graph with 6 vertices and 10 edges,minimum degrees can be 2 or 3.so,if we remove 3 edges,then graph will be disconnected