To solve the equation \(-4t + 14 = -9t + 24\), we can start by getting the terms involving \(t\) on one side and the constant terms on the other side.
- Add \(9t\) to both sides:
\[ -4t + 9t + 14 = 24 \]
This simplifies to:
\[ 5t + 14 = 24 \]
- Next, subtract \(14\) from both sides:
\[ 5t = 24 - 14 \]
This simplifies to:
\[ 5t = 10 \]
- Now, divide both sides by \(5\):
\[ t = \frac{10}{5} \]
This simplifies to:
\[ t = 2 \]
Therefore, the value of \(t\) that makes the equation true is \( \boxed{2} \).