Why More US Users Are Turning to Bank of America’s Credit Card Application

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\min |2\sin x + 3\cos x + 4| = 4 - \sqrt{13} \quad \text{if } 4 - \sqrt{13} > 0
But $ 4 - \sqrt{13} > 0 $ since $ \sqrt{13} < 4 $, so yes.
But wait: is this the minimum? Since the expression inside is always greater than $ 0 $, the absolute value is minimized exactly when $ 2\sin x + 3\cos x $ is minimized.

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