To find the voltage across a 10-ohm resistor, the discussion highlights the necessity of using circuit analysis methods beyond simple resistor reductions. The problem involves resistors in parallel and series, with a voltage source affecting the circuit configuration. Participants note that the solution in the textbook utilized source transformation, which some found unfair for the problem's level. While nodal analysis and mesh methods were mentioned, it was concluded that more complex analysis is required to arrive at the correct voltage of 14.286 volts. Ultimately, the consensus is that basic techniques alone are insufficient for this circuit problem.