3sqrt(2)*4sqrt(12)-6sqrt(54)

As follows:

Note that 12 = 2*6   and 54 = 9*6 so:

\(3\sqrt{2}\times 4\sqrt{12}-6\sqrt{54}\rightarrow 3\sqrt2\times 4\sqrt{2}\sqrt6 - 6\sqrt9\sqrt6\)

This simplifies to  \(12\times2\sqrt6-6\times3\sqrt6 \rightarrow 24\sqrt6 - 18\sqrt6 \rightarrow 6\sqrt6\)  

So the end result is 6sqrt(6)

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okay thank you Alan that helps alot