I wanted to come up with a method of solving the 4x4 edge parity without having to memorize a complicated algorithm. I found a pattern that can be broken in to three simpler sections that will solve it.

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I'm not a fan of algorithms, but here is the one I used if your brain does work that way:
Section #1: r' U2 l F2 l' F2
Section #2: r2 U2 r U2 r' U2
Section #3: F2 r2 F2

Key:
Left to right: L, l, r, R
Top to bottom: U, u, b, B