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Suppose we're given this graph, without any function definition: function plot.

And now we're supposed to find this limit.

How do you approach such problem? I know that derivative of function in [-2;0] is slope with extreme grow, but I'm not sure how to use this knowledge to count the limit. My deduction would lead me to believing it's a big number, however, I can't figure out what number exactly.

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You are probably asked to observe that the tangent to the curve is vertical there, i.e. the slope is infinite.

(Strictly speaking it is impossible to tell the slope from the plot, which is lacking accuracy, but without further information, the most sensible guess is infinity.)

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    You're correct. I was confused about not using the fact that limit is approaching -2 from left, but as you stated it's probably simplified problem. – 2017-02-27
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    @JohnSmith: hem, it is nowhere said that the limit is approaching from the left. – 2017-02-27
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Because the given function is continuous at $x=-2$, all you need to do is check what the corresponding $y$ value is.

For example, using the same graph you have included in your question, $\lim_{x\to 0} f(x) = 4$.