One such word is whenever.
airtimeanytimebedtimedowntimelunchtimemealtimeovertimeplaytimesometimespringtimesummertimetimebasetimeouttimesharewintertime
roommate
a compound word beginning with cart is any word that begins with cart and has another word in it.
quiz off
Some compound words starting with under include:underbrushunderclothesundercookundercoverundercutunderdoneunderestimateundergoundergroundundergrowthunderdevelopedunderhandedunderlineunderlyingundermineundernourishedunderpaidunderpantsunderpinningunderplayunderperformedunderratedundershortsundershotundersideunderstandunderstateunderstoodundertakeundertowunderusedunderwear
Fallback is a compound word. Falloff and fallout are compound words.
The answer is become.
A compound word starting with "drop" is "dropkick."
Doable
airtimeanytimebedtimedowntimelunchtimemealtimeovertimeplaytimesometimespringtimesummertimetimebasetimeouttimesharewintertime
zebralicious
Balloon.
backbonebackgroundballparkbaseballbaseboardbasketballbathhousebathtubbathwaterbirdhousebirthdaybirthmarkbirthrightblackbirdblackboardblackmailbloodbathbookmarkbookshelfbluebellbluebirdblueprintboyhoodbrainwavebreadwinnerbreakwaterbrownstonebutterball
mousehouse
Snail
Bankteller
maidness