Explanation for Option R :
G contains 5 vertices and 9 edges and in G 4 vertices of degree 4 and one vertex of degree 2.
So, in L(G) all vertices became edges. So 9 vertices and edges in L(G) we can get by first taking any single vertex of degree 4 in G. Degree 4 means 4 incident edges to vertex in G choose any 2 in C(4,2) ways and do this for 3 more vertex of degree 4. Now last 1 edge for L(G) is given by degree 2 in G.
So resulting = 4 * C(4,2) + 1
= 4 * 6 + 1
= 25 edges
Now rest you can check planarty by |E| <= 3|V|-6