To simplify the expression \(4\sqrt{3} + 2\sqrt{48}\), we first simplify the term \(2\sqrt{48}\):
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Factor \(48\): \[ 48 = 16 \times 3 = 4^2 \times 3 \]
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Simplify \(\sqrt{48}\): \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]
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Now substitute back into the expression: \[ 2\sqrt{48} = 2 \times 4\sqrt{3} = 8\sqrt{3} \]
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Combine like terms: \[ 4\sqrt{3} + 8\sqrt{3} = (4 + 8)\sqrt{3} = 12\sqrt{3} \]
Thus, the expression \(4\sqrt{3} + 2\sqrt{48}\) simplifies to \(\boxed{12\sqrt{3}}\).