To divide fractions, you can multiply by the reciprocal of the divisor.
So, to calculate \( \frac{2}{3} \div \frac{12}{19} \), you can rewrite this as:
\[ \frac{2}{3} \times \frac{19}{12} \]
Now, multiply the numerators and the denominators:
\[ \frac{2 \times 19}{3 \times 12} = \frac{38}{36} \]
Next, you can simplify \( \frac{38}{36} \) by finding the greatest common divisor (GCD) of 38 and 36, which is 2:
\[ \frac{38 \div 2}{36 \div 2} = \frac{19}{18} \]
So, \( \frac{2}{3} \div \frac{12}{19} = \frac{19}{18} \).