To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we first need to combine like terms.
1. Start with the equation:
\[
3m + 54 - \frac{3m}{4} = -2
\]
2. To eliminate the fraction, let's express \( 3m \) with a common denominator. We can express \( 3m \) as \( \frac{12m}{4} \):
\[
\frac{12m}{4} + 54 - \frac{3m}{4} = -2
\]
3. Combine the \( m \) terms:
\[
\frac{12m - 3m}{4} + 54 = -2
\]
\[
\frac{9m}{4} + 54 = -2
\]
4. Now, isolate the term with \( m \):
\[
\frac{9m}{4} = -2 - 54
\]
\[
\frac{9m}{4} = -56
\]
5. To eliminate the fraction, multiply both sides by 4:
\[
9m = -56 \times 4
\]
\[
9m = -224
\]
6. Divide both sides by 9 to solve for \( m \):
\[
m = \frac{-224}{9}
\]
Thus, the value for \( m \) that makes the equation true is:
\[
m = \frac{-224}{9}
\]