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Given that, $x = 4, y = 64.$

Now, $x: y :: y: \_\_\_\_ = 4: 64:: 64 : \_\_\_\_$
 
$\implies x: y :: y: \_\_\_\_= 4: 4^{3}:: 64 : 64^{3} = 4: 64:: 64 :262144.$

So, the correct answer is $(D).$
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