Cut and cycle property both asked in this question.
Cycle property states that if edge 'e' has maximum weight in some cycle of G, then that edge won't be included in mst of G.
Using this rule,
If we notice cycle ABC, maximum weight edge which is in mst is 9, that means, there must have been an edge weight strictly greater than 9 due to which this edge i.e. AB was not included in mst for G.
Since, question asks for the minimum weight of total edges, we assume this value is 10.
Using the same concept, edge ED is of weight 7.
Cut property of MST states for any cut (S,V-S) of a graph G, if there is an edge 'e' that is lightest among all the edges that cross the cut( cross the cut means one end of edge e exists in S, and another in V-S) then that edge is safe for adding to MST.
Since, we can see the cut (ABC,DEF), BE and CD cross the cut.
Since, BE is included in mst of G, this means this was lightest of all edge crossing this cut.
So, CD should have been at least 16.
So, now total weight of all edges =69