I don’t understand where it is continuous… or discontinuous at this point. The longer I look at it the more confused I get

We can see from the graph that;
It is closed at point -4 and open at -2, then open at -2 and open at 2, then closed at 2 and open at 4, open at 4 and open at 6, finally open at 6 and open at 8.
By these deductions,
Hence, the correct option is option B