Given explanation:

In the above explanation, it is written that matching number is 4 but I am getting matching number as 3 for this graph(choosing edges 1-2, 3-4 and 6-7). Please check where I am going wrong

In Matching graph no 2 edges are adjacent it means the degree of vertex is 1

So we find such vertices and edges

Let us start with 2 then we get (2-1),(3-8),(4-7),(5-6) these edges are matching so the matched number is 4

Even these edges (2-3),(1-8),(4-5),(7-6) are matching so the matched number is 4

These edges (2-5),(3-4),(1-6),(8-7) are matching so the matched number is 4

By choosing these edges we could have vertices with 1 degree