Consider the cycle $ABC$. $AC$ and $BC$ are part of minimum spanning tree. So, $AB$ should be greater than $max(AC, BC)$ (greater and not equal as edge weights are given to be distinct), as otherwise we could add $AB$ to the minimum spanning tree and removed the greater of $AC, BC$ and we could have got another minimum spanning tree. So, $AB > 9$.
Similarly, for the cycle $DEF, ED > 6$.
And for the cycle $BCDE, CD > 15$.
So, minimum possible sum of these will be $10 + 7 + 16 = 33$. Adding the weight of spanning tree, we get the total sum of edge weights
$= 33 + 36 = 69$