there are several ways in which to do this kind of problem. Given that the 2 lines are parallel, the equation of the new line will feature the same slope.
Given line: 2x + 4y = 1
New line: 2x + 4y = C (find C)
Subst. 1 for x and 2 for y: 2(1) + 4(2) = 3 + 8 = 11
Thus, the eq'n of the new line parallel to the given line is 2x + 4y = 11.