Step 1 :\(M_D = \begin{pmatrix} 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 \\ 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & ? \end{pmatrix}\)
Step 2 :\(M_D^2 = \begin{pmatrix} 3 & 2 & 2 & 2 \\ 2 & 3 & 2 & 2 \\ 2 & 2 & 3 & 2 \\ 2 & 2 & 2 & ? \end{pmatrix}\)
Step 3 :\(M_D^3 = \begin{pmatrix} 6 & 6 & 6 & ? \\ 6 & 6 & 6 & ? \\ 6 & 6 & 6 & ? \\ ? & ? & ? & ? \end{pmatrix}\)
Step 4 :i. The total number of walks starting at node d and ending at node d of length 1 is the (4,4) entry of \(M_D\), so the answer is \(\boxed{0}\).
Step 5 :ii. The total number of walks of length 2 in graph \(G_D\) is the sum of the diagonal entries of \(M_D^2\), so the answer is \(3+3+3+2=\boxed{11}\).
Step 6 :iii. The total number of walks starting at node b and ending at node c of length 3 or less in \(G_D\) is the sum of the (2,3) entries of \(M_D\), \(M_D^2\), and \(M_D^3\), so the answer is \(1+2+6=\boxed{9}\).
Step 7 :iv. To find the total number of walks starting and ending at node c of length 4 in graph \(G_D\), we need to compute the (3,3) entry of \(M_D^4\). We can use the fact that the (3,3) entry of \(M_D^2\) is 3 and the (3,3) entry of \(M_D^3\) is 6. Then, the (3,3) entry of \(M_D^4\) is \(3^2+2^2+2^2+2^2=\boxed{20}\).