Answer
$$\langle16,-1,9 \rangle.$$
Work Step by Step
$$4\langle 6,-1,1 \rangle-2\langle1,0,-1 \rangle+3\langle-2,1,1\rangle\\
=\langle 24,-4,4 \rangle-\langle2,0,-2\rangle+\langle-6,3,3\rangle\\
=\langle16,-1,9 \rangle.$$
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