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

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we first want to eliminate the fraction.

1. Multiply every term by 4 to eliminate the denominator:
\[
4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2)
\]
Simplifying, we get:
\[
12m + 216 - 3m = -8
\]

2. Combine like terms:
\[
12m - 3m + 216 = -8
\]
This simplifies to:
\[
9m + 216 = -8
\]

3. Subtract 216 from both sides:
\[
9m = -8 - 216
\]
Simplifying gives:
\[
9m = -224
\]

4. Finally, divide by 9 to solve for \( m \):
\[
m = -\frac{224}{9}
\]

Thus, the value of \( m \) that makes the equation true is:
\[
\boxed{-\frac{224}{9}}
\]