To simplify the expression \( 2(3v+9)-14-6(-5v-4) \), let's go through the steps:
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Distribute \( 2 \) into \( (3v + 9) \): \[ 2(3v) + 2(9) = 6v + 18 \]
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Distribute \( -6 \) into \( (-5v - 4) \): \[ -6(-5v) - 6(-4) = 30v + 24 \]
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Now substitute back into the expression: \[ 6v + 18 - 14 + 30v + 24 \]
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Combine like terms: \[ (6v + 30v) + (18 - 14 + 24) = 36v + 28 \]
So the simplified expression is: \[ \boxed{36v + 28} \]