I'm confused: do you want both panel to keep the relative size, or do you want one of them to be a fixed width?
Mobiles have a bunch of different aspects, so there are many possible solutions.

If you want relative width, the UIStretch has a relative size exposed in the inspector: then the red panel can just be UIAnchored to the left with its pivot to the left and a UIStretch that has relative size set to ~0.8. (80 % of the screen). The green panel can be anchored to the right with its pivot set to right and a stretch of 0.2.
Of course, when I say the "panel" I mean a background sprite on each panel, since UIAnchor and UIStretch works best on something like that. If you're trying to get two draggable panels side by side like the other question asks, then you can do the same thing, but then just read the values from the sprites I*m talking about into your Cliprange on the draggablepanels and destroy the sprites afterwards. - Sure it's a roundabout way of doing it, but it works.