Matching it means that no 2 edges are adjacent simply a vertex with degree 1
if we have a vertex with degree 0 we say not matched
In the above graph if we start with G we have 2 edges for G In matching we consider 1 edge since if both are considered we get degree of G as 2 so if we consider G-A edge then node 2 is alone and has degree 0 it makes graph to be not matched so we consider G-2 edge , A-0 edge T has edges with 0 and 1 since A-0 edge is present if we consider 0 then degree of 0 is 2 so we don't consider
we have T-1 edge then we are left with edge E-6
Totally we get (G-2),(A-0),(T-1),(E-6) so matching number is 4