I guess I'll take the microphone casually
And do my thug-izzle
What Snoop is says “take the microphone casually” this means that he is relaxing while rhyming, and when he states do my ‘thug-izzle’ he means that he will do his usual rhymes. Since Snoop has a smooth laidback flow, these lines emphasize how he is and what he is going to do on the mic.
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