To solve the equation
\[ \frac{7}{8} \left( r - \frac{5}{21} \right) = \frac{3}{2}, \]
we start by eliminating the fraction on the left side. We can multiply both sides of the equation by \(8\) to get rid of the denominator:
\[ 7 \left( r - \frac{5}{21} \right) = 8 \cdot \frac{3}{2}. \]
Calculating the right side:
\[ 8 \cdot \frac{3}{2} = 12. \]
Now we have:
\[ 7 \left( r - \frac{5}{21} \right) = 12. \]
Next, we divide both sides by \(7\):
\[ r - \frac{5}{21} = \frac{12}{7}. \]
Now to isolate \(r\), we add \(\frac{5}{21}\) to both sides:
\[ r = \frac{12}{7} + \frac{5}{21}. \]
To add these fractions, we need a common denominator. The least common multiple of \(7\) and \(21\) is \(21\). We convert \(\frac{12}{7}\):
\[ \frac{12}{7} = \frac{12 \cdot 3}{7 \cdot 3} = \frac{36}{21}. \]
Now we can add:
\[ r = \frac{36}{21} + \frac{5}{21} = \frac{36 + 5}{21} = \frac{41}{21}. \]
Thus, the solution for \(r\) is
\[ \boxed{\frac{41}{21}}. \]