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I tried to make the curve (or 2 straight lines rather) by $y = x + 3$ and $y = -x-3$, but I don't know what to do next.Is it that the area between those two lines or the whole area.

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    So, the area is $A=9$? Its the sum of two areas of having the same base=3 and height=3. Try to sketch the graph... – 2017-02-15

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The function $y=|x+3|$ equals zero at $-3$, so first you have to consider which of $y=x+3$ and $y=-x-3$ equals $y=|x+3|$ to the left of $x=-3$ and which (the other one) to the right. By drawing a graph of both $y=x+3$ and $y=-x-3$, you'll see that $y=x+3$ occurs to the right of this point.

The total area between $y=|x+3|$ and the $x$-axis between $x=-6$ and $x=0$ therefore equals the sum of the area of $y=-x-3$ and the $x$-axis between $x=-6$ and $x=-3$ and the area of $y=x+3$ and the $x$-axis between $x=-3$ and $x=0$. Both these areas are a triangle with base 3 and height 3, so the total area is twice the area of such a triangle, i.e. $2\cdot\frac{1}{2}\cdot3\cdot3 = 3\cdot3=9$.

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the area is given by $$\frac{1}{2}\cdot 3\cdot |-6+3|+\frac{1}{2}\cdot 3\cdot|0+3|=\frac{1}{2}(9+9)=\frac{18}{2}=9$$