Can you give me an example word that is in the language $L = \{w | w ∈ \{a,b\}^∗ ∧ |w|_a = |w|_b\} $ Again, the language is $L = \{w | w ∈ \{a,b\}^∗ ∧ |w|_a = |w|_b\} $
Now I'm unsure about what the '*' indicates. Whether it means that either a or b can be repeated, or only one of them or if you can repeat a pattern made of a and b.
An explanation would also be appreciated but I thought one or more examples of what would be a word in the language and what not would be quicker.
Check your definitions: $*$ is the Kleene star.

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