How would I find the total resistance of the following circuit?
Assuming total resistance means the resistance seen by the 18 volt battery, then the procedure is to successively use the formulas for series and parallel resistors. First find the series result of R5 and R6.  That resistance is then in parallel with R4.  That result is in series with R3.  Again, the result of that is in parallel with R2.  Finally this result is in series with R1. If you do the arithmetic correctly, you will get the correct result.