Assume that securitization combined with borrowing and irrational exuberance in Hyperville have driven up the value of existing financial securities at a geometric rate, specifically from $$6$ to $$12$ to $$24$ to $$48$ to $$96$ to $$192$ over a six$-$year time period. Over the same period, the value of the assets underlying the securities rose at an arithmetic rate from $$6$ to $$9$ to $$12$ to $$15$ to $$18$ to $$21.$

If these patterns hold for decreases as well as for increases, by how much would the value of the financial securities decline if the value of the underlying asset suddenly and unexpectedly fell by $$6?$

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