Density altitude is the air density expressed as an altitude above MSL. Both temperature and humidity affect air density; however, temperature has a far greater impact.
Electronic E6Bs account for the effect of humidity by using both temperature and dew point temperature, the latter of which provides a measure of the air's water vapor content (technically it measures the temperature to which the air would need to be cooled for saturation to occur).
In contrast, the simple rule of thumb provided above only addresses the impact of non-standard temperature on density altitude. However, the effect of humidity can be "roughly" approximated by multiplying the dew point temperature (in degrees Celsius) by 20 and reading the results in feet.
This correction is then added to the above temperature correction rule of thumb for density altitude. Note the correction for humidity is highly non-linear and so it provides only a rough approximation. It should only be used in the dew point temperature range of 5-30 degrees Celsius.
Details can be found in Guinn, T. A., & Barry, R. J. (2016). Quantifying the Effects of Humidity on Density Altitude Calculations for Professional Aviation Education. International Journal of Aviation, Aeronautics, and Aerospace, 3(3). http://dx.doi.org/10.15394/ijaaa.2016.1124