To simplify the expression \((a^2 - 11) + (3a^2 - 4a + 6)\), we can combine like terms.
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Start by distributing and rearranging the terms: \[ a^2 - 11 + 3a^2 - 4a + 6 \]
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Combine the \(a^2\) terms: \[ a^2 + 3a^2 = 4a^2 \]
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There is one \(a\) term: \[ -4a \]
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Now combine the constant terms: \[ -11 + 6 = -5 \]
Putting it all together, we have: \[ 4a^2 - 4a - 5 \]
So the final answer is \(\boxed{4a^2 - 4a - 5}\).