No, it's not a possible graph. We can prove this fact by using the following theorem:

Theorem: If the sequence r,s_1,s_2,...,s_r,t_1,t_2,...,t_k is a degree sequence of graph with r+k+1 vertices, then the sequence s_1 - 1,s_2 - 1,...,s_r -1,t_1,t_2,...,t_k (rearranged in a decreasing way) is a degree sequence of a graph with r+k vertices.

Step 1.a: 8|7,7,7,7,3,3,3,3|2

Step 1.b: 6,6,6,6,2,2,2,2,2

Step 1.c: 6,6,6,6,2,2,2,2,2(rearranged but remained same)

Step 2.a: 6|6,6,6,2,2,2|2,2

Step 2.b: 5,5,5,1,1,1,2,2

Step 2.c: 5,5,5,2,2,1,1

Step 3.a: 5|5,5,2,2,1|1

Step 3.b: 4,4,1,1,1,1

Step 3.c: 4,4,1,1,1,1

Now without going any further, one can show that this cannot be a degree sequence of a simple graph.