dew point and cloud bottoms

other than the heat t was a nice day in mid-Misouri - lots of fluffy
clouds with pancake-flat bottoms.

Driving with my daughter, we were talking about clouds and weather and
how there really was moisture below the clouds but the temperature was
just a bit too high to condense it.

the converstaion drifted to dew point and how each 1000 feet
represents a 4.5 degree F temperature change.

she asked, basically, 'if its 104 here and the cloud bottoms are at
6000 feet it must be (104 - 6*4.5) 77 degrees there'.

I dialed asos and the dew point was actually 63.

who can help with this calculus? does density altitude play a role in
the equation?