1. The problem is asking how much larger the expression $13x^{2} - 7y^{2}$ is compared to $6x^{2} - 9y^{2}$.\n\n2. To find the difference, subtract the second expression from the first: $$ (13x^{2} - 7y^{2}) - (6x^{2} - 9y^{2}) $$\n\n3. Distribute the subtraction sign: $$ 13x^{2} - 7y^{2} - 6x^{2} + 9y^{2} $$\n\n4. Combine like terms: for $x^{2}$ terms, $13x^{2} - 6x^{2} = 7x^{2}$. For $y^{2}$ terms, $-7y^{2} + 9y^{2} = 2y^{2}$.\n\n5. Final simplified difference: $$ 7x^{2} + 2y^{2} $$\n\nThis means $13x^{2} - 7y^{2}$ is $7x^{2} + 2y^{2}$ larger than $6x^{2} - 9y^{2}$.