First update:

Distance vector (Node A)
Node B C D E F
Distance INF 2 INF 5 INF

Recieved distance vector (Node C)
Node A B D E F
Distance 2 INF 4 2 INF

Updated distance vector (Node A)

Dist(A, x) = min(Dist(A, x), {Dist(A, C)+Dist(C, x)})

Node B C D E F
Distance INF 2 6 INF