rabbit
bedbug
beaverbeaglebeetlebaboon
There are not too many 6-syllable animal names out there. However, there are some out there, and one of them is yellow-bellied marmot.
donkey
reigns
Some six letter words with the fifth letter I are:acaciaacquitaffairafraidanemiaauntiebanditbarriobigwigbionicbobbinboogiecandidcatnipcervixcitricclericcliniccoffincolliecommitcookiecosmiccousincreditcriticculpritdahliadebrisdeceitdetaindevoiddimwitdomaineclairentaileroticethnicfabricferricforbidfrolicgarlicgerbilgossipGothichectichermitherniaheroinhorridhubrishybridiconicimpairinlaidironicitalicjerkinliquidmantismarginmarlinmemoirmohairmosaicmuffinmythicnapkinniacinnitricobtainorchidordainoriginoutfitoxtailpallidpectinpelvispencilpermitphobiapicnicpotpieprefixprofitpublicpulpitrabbitraisinrecoilremainrepairrookierusticsepticsordidspiritstaticstudiostupidsubmitsuffixsummittactictennistidbittorridtragictropicturnipurchinverminvictimviolinvirginweevilzinnia
There are no English words ending in "-six", let alone six letter words.
Some six letter words with the second letter U are:auburnaugustauricleauroraauthorautismautumnbucketbucklebudgetbuffetbufferbulletbumblebumperbundlebunglebunkerburgleburgerbutanebutlerbutterbuttoncubismcuckoocuddlecudgelcupolacurfewcurlercursorcurtsycustomcutletcutoffcutterdugoutdulcetduplexdustereulogyeunucheurekafumblefungusfunnelfurrowfusionfutilefutureguitarguiltygulletgunnergurglegussetgutterguzzlehuddlehumblehungerhunterhustlejumblejunglejunkiekuchenlumbermuddlemumblemuttermutualnudistnuggetoustedoutfitoutrunpuddlepulleypunnetpusherputterquaintqueasyrubberruggedrusticsubtlesubmitsucklesullensupplesurreytumbleturkeyturrettussleturtlevulgar
Some six letter words ending in R are:antleranswerbeaverbetterbitterborderbutlerbuttercratercursorcuterfalterfiltergarterhamperhatterhealerheaterhotterjuniorkinderladderlardermurderporterpotter
Some six letter words beginning with T are:tackletampertangletellertempertemplethirsttimbertissuetoilettonguetoppletorquetorridtrickytripletumulttundraturkeyturtle
Some six letter words with OOS in the middle:IgloosKazoosWazoosYahoos
Some six letter words that rhyme with 'sigh' are:banzaiherebysupply