It involves the concept of chromatic partitioning which says that the proper colouring of graph induces a partitioning of vertices onto the vertices of graph such that each set formed is an independent set.
So, to find chromatic partitioning of a graph G enumerate through all maximal independent set of graph G and take minimum number of these sets which collectively include all vertices of G.
The maximal independet sets of this graph are
{a,d}, {a,f}, {b,e}, {c,f}, {d,e}.
Now from among these maximal independent set of vertices we have to select minimum number of such sets which can include all vertices of graph and one such way is
{a,d} , {b,e} , {c,f}
This is the chromatic partitioning of this graph and since each one is an independent set we can assign a single colour to colour all vertices within a independent set and we need 3 colours to color these 3 sets.So our graph only needs 3 colours for proper colouring.
Hence,the chromatic number of this graph is 3.
You can include this in your answer sukanya.