Add $4 \sqrt{3}+2 \sqrt{5}$ and $6 \sqrt{3}-4 \sqrt{5}$.

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$(4 \sqrt{3}+2 \sqrt{5})+(6 \sqrt{3}-4 \sqrt{5})$

$=(4 \sqrt{3}+6 \sqrt{3})+(2 \sqrt{5}-4 \sqrt{5})$

$=(4+6) \sqrt{3}+(2-4) \sqrt{5}$

$=10 \sqrt{3}-2 \sqrt{5}$

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