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@Saurav04 You are correct. 3 guarantees it and should be the answer. If the question is modified like "remove any n number of edges and guarantees disconnection"  then 6 is the answer.

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@Arjun sir  I didn't get ur point what does this means "remove any n number of edges and guarantees disconnection"  then 6 is the answer

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That means any choice of $n$ edges should guarantee disconnection- random choosing.

Answer 1

suppose this is the graph

now if we remove edges AE,BE,BF and CE

the graph becomes this-->

So now ,to make it disconnected you only need to remove only two more edges..

so by removing any two edges the graph becomes disconnected.

Hence the answer is 6.

Comments

just remove <b c> <c e>  <c d> this will make vertice C isolated in question they have use term minimum only 3 edge are sufficient

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The question here asks minimum number of edges which can be deleted so that it always guarantees a disconnected graph...So if we take any other three edges then there is a possibility that the graph is not disconnected at all..