Left 申 — originally a pictograph of lightning streaking down, meaning 'to extend, stretch out.' In 畅 it carries the core sense of unimpeded extension that gives 'smooth, unhindered, fluent' (畅通, 畅销). Indexed under Kangxi #72 日 (rì) by tradition via the sun-shaped box inside 申.
Right side is the heavily contracted form of 昜 (standalone 9 strokes, here just 3 — the bottom kicks of the sun-rising graph survive). 昜 supplies the sound: yáng → chàng with strong drift. Same phonetic source feeds 阳 (sun), 扬 (raise), 杨 (poplar), all linked by the bright/upward image.
Filed under radical 日 (rì, #72) by convention. 日 is not a separate component in 畅, so no strokes are highlighted.
