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

Let's first isolate \(m\) in the equation \(3m + 54 - \frac{3m}{4} = -2\).

1. Combine the \(m\) terms on the left side.

To do that, we can rewrite \(3m\) as \(\frac{12m}{4}\):

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

2. Combine the fractions with common denominators:

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

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

3. Next, isolate \(\frac{9m}{4}\) by subtracting 54 from both sides:

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

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

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

\[
9m = -56 \cdot 4
\]

\[
9m = -224
\]

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

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

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

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