Answer
$$\langle-2\sqrt{2},-2\sqrt{2}\rangle.$$
Work Step by Step
Since the vector is in the direction $\langle-1,-1\rangle$, then it will be in the form $ au=\langle-a,-a\rangle $. Now, since the length is $4$, then we have
$$\sqrt{a^2+a^2}=\sqrt{2a^2}=4\Longrightarrow 2a^2=16\Longrightarrow a=\sqrt{8}=2\sqrt{2}.$$
Hence the required vector is given by the components
$$\langle-2\sqrt{2},-2\sqrt{2}\rangle.$$
