First, you are not required to use 80% when figuring the demand loads for the sub-panel. The so-called 80% rule only applies to
continuous loads, such as electric resistance heat, or electric water heaters. If none of those are connected to the sub-panel, then eliminate any use of this part of the equation. :huh:
Second, your calculation of 6x20 Amp breakers fails to recognize that your sub-panel is fed with a 120/240 feeder, which has 2 hots. Your 6x20 Amp breaker total only takes 120 Volt loads into consideration. :?
You have to divide that total by 2 to be able to calculate the loads across both hot legs..... BUT ....
The third thing you are doing here is taking the overcurrent value of the breakers, and adding them up as if they will be loaded to 100% of their rating all the time. This is not the proper way to perform load calculations. :blink:
Start over by studying section 220 of the NEC ....