You are confusing yourself.

Roll One Die Twice: P(even) = 1/2, then p(2) = 1/6, p(even and 2) = (1/2)*(1/6) = 1/12

Roll Two Dice Simultaneously: P(#1 is even) = 1/2, and p(#2 is 2) = 1/6, then p(#1 is even and #2 is 2) = (1/2)*(1/6) = 1/12

Roll One Die Once: P(even and 2) = p(2) = 1/6 -- These two events are not independent with only one roll of one die.