1. The problem asks for the number of distinct zeros of the polynomial function $$h(t) = (t - 8)^1 (t - 4)^2 (t - 2)^3 (t - 1)^4$$. 2. Recall that the zeros of a polynomial are the values of $t$ that make the polynomial equal to zero. 3. Each factor $(t - a)^n$ contributes a zero at $t = a$, regardless of the exponent $n$. 4. The distinct zeros are the unique values of $t$ from each factor. 5. From the given polynomial, the zeros are at $t = 8$, $t = 4$, $t = 2$, and $t = 1$. 6. Counting these unique zeros, we have 4 distinct zeros. Therefore, the polynomial function $h(t)$ has **4 distinct zeros**.