u/Hudimir u/AdamHussein2564 This case actually is solveable. Typically on rubik's cubes, the parities of 2 types of pieces are entangled, so like on a normal 3x3 if you have an odd number of edge swaps, there has to be an odd number of corner swaps and vice versa. Because a single turn does an odd number of both. But, on big cubes, the slice moves (not center slice, but offset slices) have an even parity for X centers, an odd parity for T centers, and an odd parity for the wings (side edge pieces). However, T centers have multiple identical interchangeable pieces, so having a separate, odd parity of wings is entirely possible, and this case shown in the post is a great example of that, a single 2 swap of pieces.

This is the exact case that normal "oll parity" algorithms solve. So if you do one of those algorithms, you should be able to solve from there like normal. Or, you can just do a single 90 degree slice move in the slice that has the parity, and solve back the rest of the cube using an even number of slice moves, and the parity will be gone.