"reallyhoping"isveryinformal.Inadditiontothat,there'sagrammaticalmistakeinit."Ireallyhoping"shouldbeIAMreallyhoping.
Ifthisisforaformalreportorforsomeotherspecialoccasion,theword"really"soundsextremelyinformalandthusimpolite.Therefore,"Idohope"ismoreestablishedthan"reallyhoping."
SorryI'mfromtheUnitedStatesandIdon'tknowhowtotypeinChinese.