Pepper will not dissolve in water.
Add the mixture into water and stir to dissolve the sugar. Pour the watery mixture into another container, using a paper filter to catch the pepper. If you would like to have the sugar back into solid form, simply evaporate the water.
Dissolve the mixture in pure water. Run the water through a filtration system. All the pepper should be trapped in the filter and you will need to allow this to dry. The water that runs through the filter should contain all the sugar - in solution. It will be necessary to allow this water to evaporate - either in its own time or by evaporation. However, you may end up with sugar crystals that are quite different (in size) from those in the sugar-pepper mixture.
Sugar solution
Pepper and water is not a solution, it is a mixture because the pepper will not dissolve. If you're wondering if salt and water is a solution, it is because it's the solution saltwater and the salt does dissolve unlike the pepper.
First put the mixture in a colander and separate the salt and pepper from the pebbles. Then put the salt and pepper in water and stir it to dissolve the salt. The pepper will not dissolve, and you can remove the pepper. Then allow the water to dissolve and you will be left with the salt.
Pure sugar is a compound, which is a pure substance. If you dissolve sugar in water, you will have a homogeneous mixture, which is a solution.
Dissolve the sugar in water and then evaporate the water
Pour the mixture into enough water that all the sugar will dissolve. Sand does not dissolve in water, so the sand will settle to the bottom of the solution and then you can sift the sand out of the solution. Then you will just have sand and sugar water, which can evaporate, leaving the sugar behind in the container.
Both. A solution is a mixture.
mixture dissolve in a water
It can't because of the solid particles of the pepper. This mixture is called a suspension.
This would be a mixture, because you could easily separate the water and sugar again by boiling the water.