There are 433 4-letter words containing H in the ENABLE dictionary — 11% of all 3,903 words at this length. At 4 points, H is worth more than most tiles without being awkward enough to hold back for — it is generally better placed than saved.
The H falls in the first position more often than any other, in 189 of them. 10 of them use the letter more than once — haha, hahs, hash, hath among them, which is the case worth checking twice when a game has told you a letter is present but not how many times.
If you know more than one letter, this page stops being the fast way to find it. Enter what you have in the unscrambler — the Contains, Starts with and Ends with filters combine, and setting both length fields to 4 narrows this list to the handful your letters actually allow.
Where the H sits
H in the first position (189)
haaf haar habu hack hade hadj haed haem haen haes haet haft hags haha hahs haik hail hair haji hajj hake hale half hall halm halo halt hame hams hand hang hank hant haps hard hare hark harl harm harp hart hash hasp hast hate hath hats haul haut have hawk haws hays haze hazy head heal heap hear heat hebe heck heed heel heft hehs heil heir held hell helm helo help heme hemp hems hens hent herb herd here herl herm hern hero hers hest heth hets hewn hews hick hide hied hies high hike hila hili hill hilt hind hins hint hips hire hisn hiss hist hits hive hoar hoax hobo hobs hock hods hoed hoer hoes hogg hogs hoke hold hole holk holm holp hols holt holy home homo homy hone hong honk hons hood hoof hook hoop hoot hope hops hora horn hose host hots hour hove howe howf howk howl hows hoya hoys hubs huck hued hues huff huge hugs huic hula hulk hull hump hums hung hunh hunk huns hunt hurl hurt hush husk huts hwan hyla hymn hype hypo hyps hyte
H in the second position (119)
ahem ahoy bhut chad cham chao chap char chat chaw chay chef chew chez chia chic chid chin chip chis chit chon chop chow chub chug chum dhak dhal dhow ghat ghee ghis khaf khan khat khet khis mhos ohed ohia ohms phat phew phis phiz phon phot phut rhea rhos rhus shad shag shah sham shat shaw shay shea shed shes shew shim shin ship shit shiv shmo shod shoe shog shoo shop shot show shri shul shun shut thae than that thaw thee them then thew they thin thio thir this thou thro thru thud thug thus wham whap what whee when whet whew whey whid whig whim whin whip whir whit whiz whoa whom whop whys