The correct spelling of the phrase "putting the hospital" is /ˈpʊtɪŋ ðə ˈhɑːspɪtl/. The word "putting" is spelled with two t's and a single "u" because it is derived from the verb "put," which follows this spelling convention. "Hospital" is spelled with a silent "h," and the stress falls on the second syllable. These spelling nuances can be difficult to master, but they are crucial for effective communication and clear writing.