To find the y-intercept of a function, we substitute $x = 0$ into the function $g(x)$ and solve for $g(0)$.

Given: $g(x) = 3x^2 + 6x + 3$

Substitute $x = 0$: $g(0) = 3(0)^2 + 6(0) + 3 = 3$

So, the y-intercept of $g(x)$ is: $(0, 3)$

The correct answer is: c. (0, 3)

Would you like further explanation or details on this process?

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Here are some related questions:

1. How do you find the x-intercepts of a quadratic function?
2. What is the vertex of the function $g(x) = 3x^2 + 6x + 3$?
3. How does the value of $a$ in $ax^2 + bx + c$ affect the shape of a quadratic graph?
4. How do you determine if a quadratic function opens upward or downward?
5. Can the y-intercept be used to determine the axis of symmetry?

Tip: The y-intercept of any function $f(x)$ is simply $f(0)$.