尽管
jǐnguǎn · HSK 5
even though
尽 = exhaust/utmost + 管 = tube/manage; together = 'despite all control'
尽 means to the utmost or exhaust; 管 means to manage or care about. Combined, 尽管 literally reads as 'no matter how much you manage' — i.e. regardless, even though. Also used to mean 'feel free to' (go ahead despite concerns).
尽 — hand 彐 holding brush over fire 灬
Originally depicted a hand holding a brush sweeping out the last embers in a vessel, suggesting 'finishing' or 'using up.' The simplified form 尽 replaces the older 盡, but keeps the core meaning of exhausting or completing something fully.
管 — bamboo radical 竹 + official 官 (phonetic)
Originally a pictograph of a bamboo tube or pipe, written with the bamboo radical 竹 on top. The lower component 官 supplies the sound. From 'bamboo pipe' it extended to 'tube,' then to 'manage' or 'control' — since pipes channel and regulate flow, the meaning shifted toward administration.