To solve this inequality, we need to simplify both sides and then find the values of x that satisfy the inequality.

Starting with the left side of the inequality:

H³ - 3x² + 2x - 6

This can be simplified to:

H³ - 2x² + 2x - 6

Now simplifying the right side of the inequality:

2x² - x² + x⁴ - 2

This simplifies to:

x⁴ + x² - 2

Therefore, the inequality becomes:

H³ - 2x² + 2x - 6 > x⁴ + x² - 2

Combining like terms, we get:

-x⁴ - 3x² + 2x - 4 > 0

Now we need to find the values of x that satisfy this inequality. This is a quadratic inequality, so we can find the critical points by setting the expression equal to zero:

-x⁴ - 3x² + 2x - 4 = 0

We can solve this equation to find the critical points. Once we have the critical points, we can test a value in each interval to determine which intervals satisfy the inequality.

I hope this helps! Let me know if you need further assistance.