Let's simplify the expression step by step:
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Start with the original expression: \[ 2(3v + 9) - 14 - 6(-5v - 4) \]
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Distribute the 2 in the first term: \[ = 6v + 18 - 14 - 6(-5v - 4) \]
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Simplify the constants: \[ = 6v + 18 - 14 = 6v + 4 \]
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Now distribute the -6 in the last term: \[ = 6v + 4 + 30v + 24 \]
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Combine like terms (6v and 30v; 4 and 24): \[ = (6v + 30v) + (4 + 24) = 36v + 28 \]
Thus, the simplified expression is: \[ \boxed{36v + 28} \]