申し入れる
もうしいれる · moushiireru · JLPT N1 · verb-ichidan
to propose
申 (report) + し入れる: to put forward a proposal, like going to someone with an offer
申し入れる is 申し (humble 'say') + 入れる (put in). You put a proposal into someone's hands. Roughly: 'to put forth' a suggestion formally.
入 — single pictograph, two slanting strokes
入 is a pictograph showing an arrowhead or pointed entrance, with two strokes converging downward to suggest something going inward. The original sense was 'to enter,' and it still carries that meaning today. It contrasts visually with 人 (person), where the strokes cross differently at the top.