This is the equation:
f(x) = \begin{cases} 4/3(x+3)(x+1), & \text{$x$ < 0} \\ 4, & \text{0 $\le$ $x$ $\le$ 2} \\ -2x + 8 &\text{$x$ $\ge$ 3} \end{cases}
Let's just you get given graph of this equation and you're asked to find the equation. How would you know if the coordinate (0,4) belongs to the parabola or the linear function?
EDIT: And also does anyone have any strategies that I should be using while approaching question like this because these type of questions seem to be the ones I get wrong a lot.
EDIT 2: Does anyone know where I can challenging questions like this? because they're in my exam and I've pretty much done all the questions inside my textbook similar to this difficulty and the ones in practice exams but need more.
It does not matter. You can include (0, 4) in either interval. The reason for this is fairly simple: A function is completely described by it's input (domain), and the output (range) for each value of the input. For example, if we define a function $$f(x) = \left\{\begin{aligned}&1&&; x= 1\\&1&&;x=-1\end{aligned}\right.$$ then it doesn't matter how we compute $f(x)$ as long as it behaves the same way. We can also write $$f(x) = 1 ; x=-1,1$$ or $$f(x) = x^2 ; x = -1,1.$$ All three of these definitions are equal. The function contains $(1, 1)$ and $(-1, 1)$ and is undefined everywhere else.
More directly applied to your problem, this means that you can put $(0, 4)$ with either the parabola or the linear function. Either way, the function evaluates to $4$ at $0$, and this is all that we care about. Both ways all inputs to the function provide the same output, and this is all that matters.