beak
喙 centers on the beak of a bird, the hard projecting mouthpart used for pecking and feeding.
喙 combines 口 (mouth) with 彖, which likely contributes the sound and relates to a pig's snout, together suggesting a projecting mouthpart like a beak.
The left side is a mouth 口, and the right side 彖 resembles a pig's snout. Picture a bird's beak as a hard, projecting mouth like a tiny snout.
For カイ, imagine a bird's beak snapping shut with a sharp 'kai!' sound, like the cry of a seagull: kai -> カイ.