German · Pronunciation Guide
MURK-likh with a long ö. The written g hardens to a k because it lands at the end of a syllable.
MÖG- carries the beat and -lich carries none of it. The syllable boundary is what makes this word interesting: because the suffix begins with a consonant, the g gets stranded at the end of the first syllable and hardens there, which is a devoicing you can hear inside a word rather than only at its edge.
Listen: möglich
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Das ist leider nicht möglich.
Unfortunately that's not possible.
Listen: Das ist leider nicht möglich.
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Das ist leider nicht möglich stacks two soft palatal hisses at the end, one closing nicht and one closing möglich. Leider carries the 'eye' diphthong and the softened -er ending, giving 'LY-duh', so the sentence moves from a diphthong through a hiss to a rounded vowel and out on another hiss.
Most learners keep the g voiced and say 'MUR-glikh', splitting the word as mö-glich. German splits it as mög-lich, which strands the g and hardens it to k. Add the usual ö difficulty on top — English speakers substitute the vowel of burn, which brings an r that has no place here — and the word needs both fixes to sound right.