If y - 1 is a factor of the polynomial \(y^3+ 4y^2+ ky - 6\), then the polynomial must be divisible by y - 1. We can use polynomial long division or synthetic division to divide the polynomial by y - 1 and find the remainder. If the remainder is zero, then y - 1 is a factor of the polynomial.

Alternatively, we can use the Factor Theorem, which states that if a polynomial f(x) has a factor (x - k), then f(k) = 0. In this case, if y - 1 is a factor of the polynomial \(y^3+ 4y^2+ ky - 6\), then setting y = 1 in the polynomial should give us a value of zero:

\(1^3 + 4(1)^2 + k(1) - 6 = 0\)

Solving for k, we get:

\(k = 6 - 1 - 4 = 1\)

Therefore, the value of k is 1.