The graph of f(x) = x3 + 6x2 + 12x + 8 is shown. Based on the graph, how many real number solutions does the equation x3 + 6x2 + 12x + 8 = 0 have?

You didn't show the graph.
Anyway, that equation is a perfect cube and equals
(x +2)^3
or (x +) * (x +) * (x +)
Therefore, it has 3 real number solutions and ALL of those solutions equal -2