The inner core is indeed hotter than the outer core. However, the PRESSURE on the inner core is greater than the pressure on the outer core and the melting point of iron, the main constituent of the core, INCREASES as the pressure goes up. So, because the pressure effect overrides the temperature effect, the inner core is solidified.

We also can speculate that the inner core began to freeze (solidify) about 1 or two billion years ago. the inner core makes up only 1% of the mass of the Earth; the outer core makes up about 32% of the mass of the Earth.

The inner core is solid because it is made of very dense, or heavy, materials - like iron and nickel. Even though it is very hot, these materials don't "melt" very easily, so they stay solid.

It turns out that many materials can be a solid at a higher temperature if the pressure is also higher. So, even though it is hotter in the inner core, the pressure in the core is also higher, and you can have solid iron-nickel instead of liquid.