find the maximal matching for a graph

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I'm studying for a theory exam. And I don´t understand how maximal matchning for biparte graph works. Could someone explain how I can find maximal matchning for example for this graph or some graph without weigts. I understand that i can for example start with 2-c and I see that a and b is not matched but i don´t understand which I have to choose and how I have to match them later. graph

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For graphs of this small size, a maximum matching can usually be found through a bit of trial and error. As you said, let's match 2 with $c$. Now, 1 has to be matched with either $a$ or $b$, let's go with $a$, allowing us to match 3 with $b$. The rest should be straightforward. Note that the sides of the bipartition have different sizes, so we cannot hope for a perfect matching. A maximum matching for this graph will have size 5.