深刻
しんこく · shinkoku · JLPT N3 · na-adj
serious
深刻 = deep + carve: cut so deep it is serious
深 (shin) means deep and 刻 (koku) means to carve or engrave. A problem that is 深刻 has cut in deeply, so it is serious or grave. The same 刻 appears in 彫刻 (chōkoku, sculpture) and 時刻 (jikoku, time).
深 — water radical 氵 + 罙 (phonetic, depth)
深 combines the water radical 氵 with 罙, which depicts a hand reaching into a cave or hollow. Originally it described deep water, then broadened to mean 'deep' in any sense — distance, color, or feeling. The 氵 gives the meaning, while 罙 hints at both sound and the idea of reaching far in.
刻 — knife radical 刂 + 亥 (phonetic)
A semantic-phonetic compound. The right side 亥 supplies the sound, while the knife radical 刂 on the right gives the meaning, since 刻 originally referred to carving or engraving with a blade. From 'to carve' it extended to marking time notches on a sundial, hence the modern sense of 'a moment' or 'quarter hour'.