A Pythagorean triple consists of three positive integers \( a, b, c \) such that \( a^2 + b^2 = c^2 \). Let's check each option:
A. \( (6, 8, 10) \) \[ 6^2 + 8^2 = 36 + 64 = 100 = 10^2 \] This is a Pythagorean triple.
B. \( (9, 12, 15) \) \[ 9^2 + 12^2 = 81 + 144 = 225 = 15^2 \] This is a Pythagorean triple.
C. \( (4, 6, 7) \) \[ 4^2 + 6^2 = 16 + 36 = 52 \quad \text{and} \quad 7^2 = 49 \] This does not satisfy the equation \( a^2 + b^2 = c^2 \). Hence, this is not a Pythagorean triple.
D. \( (5, 12, 13) \) \[ 5^2 + 12^2 = 25 + 144 = 169 = 13^2 \] This is a Pythagorean triple.
The option that is not a Pythagorean triple is C. (4, 6, 7).