Here are the steps to tackle this problem:

Note that for a 6th degree polynomial, the polynomial will be negative between pairs of roots if it starts from positive at negative infinity (and will alternate), or will start from negative if the leading coefficient is negative.

If you are looking for x-values (not necessarily roots) that result in positive y-values, steps 1 and 2 should be sufficient.

Without a specific polynomial, it's challenging to provide a more detailed step-by-step process, but this approach should work in general. Please replace the general terms with your specific polynomial coefficients. If the polynomial or further specifics are known, additional or alternative steps might be required.