Ok, I'll try. But it is very hypothetical. Typically a king is not chosen by the people. In fact I think that is part of the definition of a king and queen that they are not elected. Having said that, there are many forms of monarchy including democracies where the monarch has only ceremonial functions or very limited real political power. Canada is an example. There are many others.

A monarchy can be a democracy if it is what is called a constitutional monarchy. The constitution could be written or unwritten.

Some of the things that characterize a democracy are free elections, free press, an (independent) judicial system, a constitution of sorts. You get the idea. So a monarch who is typically in power for life and who makes all the decisions, laws etc is not a democracy. A monarch who is elected by the people and who has to run for re-election after a term is up and who is bound by a constitution could be considered a representative democracy as it would be the people who choose their representative and the people who could remove that representative from power. All that goes against the definition of what a Monarch is, though. So a Monarchy can really only be a democracy if the Monarch has very limited real power and the important decisions such as law making are made by elected representatives, or, less likely and less desirable, directly by the people. Most democracies around the world are a representative democracy and some may also have a monarch as the formal head of state but with little to no real political powers.