1mm of hg pressure is supposed to be the extra pressured exerted by a column of mercury 1 mm high.
So the weight of the column of mercury = density * height * Area * g
Area is the cross sectional area of the tube holding mercury.
Pressure exerted by this column = Weight / area
= density * height * g
= 13.6 * 10³ kg /m³ * 1* 10^-3 m * 9.81 m/sec²
= 133.416 Pascal or Newton/meter²
Height = 1mm (of mercury) column in the barometer.