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How far upward from its initial position does the mercury in the right arm rise?

So far, this is my work:

Using pressure = density(water) x g x height(water column) and neglecting atmospheric pressure as both sides would experience it, I equated that equation to p = density(Hg) x g x height as they would equal on the horizontal axis. I found the height to be 14.7 mm but that answer is not correct.

I am confused and have gone at this in a number of ways. I know that the value 14.7 is not the difference between the new position and the initial position and so I've kind of hit a road block. Any input or thought or help would be appreciated!