To identify the correct graph of $f(x) = x^3 + 5x^2 + 8x + 6$, let us analyze the key features of this cubic function:

1. End Behavior:

   • Since the leading term is $x^3$, the graph has an end behavior of:
     • As $x \to -\infty$, $f(x) \to -\infty$
     • As $x \to +\infty$, $f(x) \to +\infty$

2. Y-Intercept:

   • The y-intercept is determined by $f(0) = 6$, so the graph passes through $(0, 6)$.

3. Critical Points (General Observation):

   • The derivative, $f'(x) = 3x^2 + 10x + 8$, provides critical points.