Probably from chanak in the sense of tasting; properly, the palate or inside of the mouth; hence, the mouth itself (as the organ of speech, taste and kissing) -- (roof of the) mouth, taste.
see HEBREW chanak
חֵךְ noun masculine palate, roof of mouth, gums (Late Hebrew id.; Aramaic חִכָּא Arabic palate, roof of mouth, jaws, lower part of mouth, lower jaw of horse, mouth, etc. Lane659 Dozyi. 332); — absolute ׳ח Job 12:11; 34:3; suffix חִכִּי Proverbs 8:7 6t., חִכְּךָ Hosea 8:1, חִכֶּ֑ךָ Ezekiel 3:26; Proverbs 24:13; chiefly in poetry, especially Wisdom Literature: — חִכֵךְ Cant 7:10, חִכּוֺ Lamentations 4:4 2t., חִכָּהּ Proverbs 5:3, חִכָּם Job 29:10; — palate, roof of mouth:
a. שֹׁפָר אֶלחִֿכְּךָ Hosea 8:1 a trumpet to thy palate! (or gums; as in English, to thy lips); often with לָשׁוֺן, tongue clings (דבק) to חך, expression for speechlessness Ezekiel 3:26; Job 29:10, as imprecation Psalm 137:6; for the parching of extreme thirst Lamentations 4:4 (בַּצָּמָא), compare Psalm 22:16 כֹּחִי כַּחֶרֶשׂ יָבֵּשׁ ᵑ0 read חִכִּי for כחי see Checritical note ("" מַלְקוֺחָ֑י מֻדְבָּק לְשׁוֺנִי).
c. as organ of taste Job 12:11; 34:3, לְחִכִּי מָתוֺק מִּרְיוֺ Song of Solomon 2:3 his fruit was sweet to my palate, Proverbs 24:13 (implied simile of wisdom as sweet to the soul); figurative of God's words as sweet ׳לְח Psalm 119:103 ("" מִּי); of taste as distinguishing misfortunes Job 6:30 ("" לָשׁוֺן; > others of speech); of keeping wickedness ח ׳בְּתוֺךְ 20:18 ("" לָשׁוֺן תַּחַת), i.e. delighting in and prolonging the taste of it.