The ability of cells to pass on their characteristics to new cells is most directly related to the ability of

The ability of cells to pass on their characteristics to new celss is most direclty related to the ability of "the chromosomes to replicate."

Explanation:

First of all, let's analyze all the options:

Mitocrondria's release of energy is not related to DNA replication. Even though they have DNA and they are the core of the cell the DNA from the cellular division is not taken from it. So it's incorrect.

Chloroplast to capture energy. Well if this would be the case, animals couldn't have cell replication or reproduction because only plant cells' have chloroplasts. So it's wrong.

Cytosol to release waste is incorrect also because waste is not employed in the reproduction process.

And finally, chromosomes to replicate, because the DNA chain is divided and then two identical chains of chromosomes grow to two different cells.

just go with your heart buddy