$$4 \times \sqrt{ 2 } -3 \times a \times (- \sqrt{ 2 } )= \sqrt{ 2 }$$
$a=-1$
$$4\sqrt{2}-3a\left(-1\right)\sqrt{2}=\sqrt{2}$$
$$4\sqrt{2}+3a\sqrt{2}=\sqrt{2}$$
$$3a\sqrt{2}=\sqrt{2}-4\sqrt{2}$$
$$3a\sqrt{2}=-3\sqrt{2}$$
$$3\sqrt{2}a=-3\sqrt{2}$$
$$\frac{3\sqrt{2}a}{3\sqrt{2}}=-\frac{3\sqrt{2}}{3\sqrt{2}}$$
$$a=-\frac{3\sqrt{2}}{3\sqrt{2}}$$
$$a=-1$$
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