Simplify (21x2)/(8xy) / (7xy)/(12x2)

To divide by a fraction, multiply by its reciprocal.

$$\frac{21x^2}{8xy} \div \frac{7xy}{12x^2} = \frac{21x^2}{8xy} \times \frac{12x^2}{7xy}$$

Multiply the coefficients and add the exponents for like variables.
Numerator: $21 \times 12 \times x^2 \times x^2 = 252x^{2+2} = 252x^4$
Denominator: $8 \times 7 \times x \times x \times y \times y = 56x^{1+1}y^{1+1} = 56x^2y^2$
So the expression becomes:

$$\frac{252x^4}{56x^2y^2}$$

Divide the numerical coefficients: $\frac{252}{56}$. Both are divisible by 7: $252 \div 7 = 36$, $56 \div 7 = 8$. So $\frac{36}{8}$. Both are divisible by 4: $36 \div 4 = 9$, $8 \div 4 = 2$. So $\frac{9}{2}$.
Simplify the $x$ terms: $\frac{x^4}{x^2} = x^{4-2} = x^2$.
The $y$ terms are only in the denominator: $\frac{1}{y^2}$.
Combining these simplified parts:

$$\frac{9x^2}{2y^2}$$