He was quite quiet and I offered to take him somewhere but he said he was fine and he'd just go go home and change clothes.'
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quite /kwat/ adv. and quiet /kwat/ adj. I have no problem with /kwat/ because it is easy to be pronounced. However, /kwat/ is difficult since we have diphthong /a / followed by near-close near-front unrounded vowel /I/.
For most speakers of BrE, the final vowel in 'quiet' is /ə/, not /ɪ/. If your vowel in the second syllable is /ɪ/, the glide from the diphthong to the vowel is the same as that in 'crying', 'flying', 'buy it'. etc.