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

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we will first simplify it.

1. Combine like terms. We can rewrite \( 3m \) as \( \frac{12m}{4} \) to have a common denominator:

\[
\frac{12m}{4} - \frac{3m}{4} + 54 = -2
\]

2. Combine the terms with \( m \):

\[
\frac{12m - 3m}{4} + 54 = -2
\]
\[
\frac{9m}{4} + 54 = -2
\]

3. Next, we will isolate the \( \frac{9m}{4} \) term. Subtract 54 from both sides:

\[
\frac{9m}{4} = -2 - 54
\]
\[
\frac{9m}{4} = -56
\]

4. Now, to eliminate the fraction, multiply both sides by 4:

\[
9m = -56 \times 4
\]
\[
9m = -224
\]

5. Finally, divide by 9 to solve for \( m \):

\[
m = \frac{-224}{9}
\]

Thus, the value for \( m \) that makes the equation true is:

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