To divide the two fractions given, we can use the rule that states that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we have:
\[ \frac{2 - j}{15} \div \frac{j - 2}{21} = \frac{2 - j}{15} \times \frac{21}{j - 2} \]
Next, we can simplify this expression. We notice that \(j - 2\) is the same as \(-(2 - j)\). Therefore:
\[ \frac{21}{j - 2} = \frac{21}{-(2 - j)} = -\frac{21}{2 - j} \]
Substituting this back into our expression gives:
\[ \frac{2 - j}{15} \times -\frac{21}{2 - j} \]
The \(2 - j\) terms cancel out:
\[ -\frac{21}{15} \]
Now, we simplify \(-\frac{21}{15}\). The greatest common divisor (GCD) of 21 and 15 is 3:
\[ -\frac{21 \div 3}{15 \div 3} = -\frac{7}{5} \]
Thus, the final answer in lowest terms is:
\[ \boxed{-\frac{7}{5}} \]