Can you give me an example word that is in the language $L = \{w | w ∈ \{a,b\}^∗ ∧ |w|_a = |w|_b\} $
Check your definitions: $*$ is the Kleene star.

So, $\{a,b\}^*$ is the set of all finite strings over alphabet $\{a,b\}$.