Imagine that black ash from multiple volcano eruptions made photosynthesis impossible anywhere on Earth for many years. What would be the consequences to plants and animals? How would microbes (bacteria and Archaea) be affected?

Without Photosynthesis plants and animals won't exist.

Explanation:

Photosynthesis is a process through with plants and other living things makes food. It is a chemical reaction which is endothermic in nature that uses sunlight to turn Carbon dioxide into sugar,in order for the cells to use to perform Work.

The occurance of volcano as described in the question happens to disrupt the Continuous occurance of photosynthesis and this in turn will greatly affect the existence of plants and animals. We can simply say plants and animals can not exist without Photosynthesis.

This is because photosynthesis releases a large amount of oxygen into the atmosphere , of which both plants and animals make use of.

If I may ask how do you feel staying in an atmosphere with limited supply of oxygen ? Of course you feel suffocated and you feel you are dieing. That is exactly the scenario we are analysising now.

Some group of sea organism that doesn't depends on photosynthesis will still survive never the less. But organisms that takes in Oxygen and gives out Carbondioxide have a higher rate of not surviving.

the answer would be   10%