What value will make the equation 3m+54−3m4=−2

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), let's first simplify and combine like terms.

1. **Rearrange the equation**:
\[ 3m + 54 - \frac{3m}{4} = -2 \]

2. **Combine the \( m \) terms**:
To combine \( 3m \) and \(-\frac{3m}{4}\), first convert \( 3m \) to a fraction with a denominator of 4:
\[ 3m = \frac{12m}{4} \]
Therefore,
\[ \frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4} \]

3. **Substituting back into the equation**:
\[ \frac{9m}{4} + 54 = -2 \]

4. **Isolate the term with \( m \)**:
Subtract 54 from both sides:
\[ \frac{9m}{4} = -2 - 54 \]
\[ \frac{9m}{4} = -56 \]

5. **Solve for \( m \)**:
To eliminate the fraction, multiply both sides by 4:
\[ 9m = -56 \times 4 \]
\[ 9m = -224 \]
Now divide by 9:
\[ m = \frac{-224}{9} \]

Thus, the value that will make the equation true is:

\[
\boxed{\frac{-224}{9}}
\]