To solve this equation, we first need to convert the mixed numbers to improper fractions.

8 4/9 = 8 + 4/9 = 8(9/9) + 4/9 = 72/9 + 4/9 = 76/9

3 7/9 = 3 + 7/9 = 3(9/9) + 7/9 = 27/9 + 7/9 = 34/9

Now, the equation becomes:

76/9 - m = 34/9

Next, we need to isolate the variable 'm' by subtracting 76/9 from both sides:

-m = 34/9 - 76/9

-m = (34 - 76)/9

-m = -42/9

Finally, divide by -1 to get the value of 'm':

m = 42/9

m = 14/3

Therefore, the solution is m = 14/3.