How to Trace Path in Proof that Regular Languages are Closed Under Reversal
Whether a proof is sufficiently detailed is in part a question of taste. Your last statement is very general and with little detail. A more detailed argumentation could be like this:


Let the path from $q_0$ to $q_{acc}$ go through the sequence of states $q_0 -&gt; q_1 -&gt; ... -&gt; q_{n-2} -&gt; q_{n-1} -&gt; q_{acc}$.
Transition $q_{n-1} -&gt; q_{acc}$ reads the letter $w[n]$ (w has length n) which is equal to $w^R[1]$. According to the third clause in the definition of $\delta'$ there is a transition $\delta'(q_{acc},w[1]) = q_{n-1}$ which can start a path for $w^R$ in M.
Now you can continue by induction or by simply stating that the same is true for every transition in the path for $w$. At any rate, since your construction is on the level of transitions, your argumentation should go down to the level of transitions somewhere and not stop at the level of paths.