Explanation:
if I understand your typing correctly, and there is nothing missing, we have
f(x) = 0.6x⁵ - 2x⁴ + 8x
the "end behavior" means the general tendency of the result values for very large or very low values of x (going to +infinity and -infinity).
the higher (or lower in the negative direction) x gets, the more the highest exponent will dominate the result values.
it does not matter, that it has a diminishing factor (or coefficient) like 0.6.
the much stronger progression of x⁵ vs. smaller exponents like x⁴ or x will easily compensate for that with sufficiently large x.
so, ultimately, the term with the highest exponent (in our case 0.6x⁵) defines the end behavior.
with x going to +infinity, so does the function result (+infinity).
with x going to -infinity, so does the function result (-infinity, because an odd exponent number like 5 will maintain the sign of the argument).