Question

6:180 : 9: _ find missing number options are 729 738 632 648 623

Answer 1

If your question is 6:180::9: __; then 
let the number be x. 
$6:180::9: x\\ \\ \Rightarrow \frac{6}{180} = \frac{9}{x} \\ \\ \Rightarrow x=9 \times \frac{180}{6} \\ \\ \Rightarrow x=\boxed{270}$

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But there is no option of 270. 
So If you want a number from the options;

6²(6-1) = 180
9²(9-1) = 81×8 = 648

648 is the missing number.