Daniel B. answered 10/27/20
A retired computer professional to teach math, physics
Let the density of the liquid on the right be x.
Since the mercury has the same height on left and right, it experiences
the same pressure.
The liquids on the left and right exert pressure proportional to the product
of their height and density (see below). Therefore
993cm . 866kg/m^3 = 667cm . x
x = 993 . 866 / 667 kg/m^3 = 1289 kg/m^3
This is the reason for my statement that pressure is proportional to
the product of height and density:
pressure = force / surface
force = mass . g (g is gravitational acceleration)
mass = volume . density
volume = surface . height
Therefore
pressure = surface . height . density . g / surface
= height . density . g