The degree of a polynomial is the highest power of the variable with a non-zero coefficient. In the given polynomial \(P(x) = 11x^8 - 5x^6 + 4x^4 - 7x^2 + 6\), the highest power of \(x\) is 8. Therefore, the degree of \(P(x)\) is 8.
Thus, the correct answer is option (1).