To simplify the expression \( -\frac{3}{4}r + 3 - \frac{5}{6}r - 6 \), you should combine like terms, which means combining the r terms and the constant terms separately. Let's combine the r terms first:
To combine the coefficients of r (\(-\frac{3}{4}\) and \(-\frac{5}{6}\)), you need a common denominator, which is 12 in this case. Convert each fraction to have a denominator of 12:
\[
-\frac{3}{4}r = -\frac{3 \times 3}{4 \times 3}r = -\frac{9}{12}r \\
-\frac{5}{6}r = -\frac{5 \times 2}{6 \times 2}r = -\frac{10}{12}r
\]
Now, combine the r terms:
\[
-\frac{9}{12}r - \frac{10}{12}r = -\frac{9+10}{12}r = -\frac{19}{12}r
\]
Next, combine the constant terms (3 and -6):
\[
3 - 6 = -3
\]
Combining the simplified r terms with the simplified constant terms, the final simplified expression is:
\[
-\frac{19}{12}r - 3
\]