Please explain what Stuart Hall means when he defines multiculturalism as ‘strategies and policies adopted to govern or manage the problems of diversity and multiplicity which multi-cultural societies throw up’ (Hall, 2000:209)

One problem that you might be having with Hall’s definition is that it does not fit with the way we laypeople (non-academics) typically understand the idea of multiculturalism.  To us, multiculturalism tends to mean the acceptance of a variety of different cultures within one society.  In other words, we tend to think that multiculturalism is the opposite of the “melting pot” model of society in which people who come to a country assimilate into that country’s dominant culture.  For us, multiculturalism is having to choose whether we want to hear English or Spanish from a computerized voice when we call for customer service.  It is seeing Muslim women wearing head scarves instead of just dressing like American women.  Multiculturalism, then, is simply the fact of having many cultures within our one society.
The problem is that this is not the type of multiculturalism that Hall is talking about in this quote.  In the article in this link, we are given a fuller definition of multiculturalism.  It tells us that multiculturalism

also stands for a desire to find the cultural and political norms appropriate to more heterogeneous societies within and across nations…

This is the type of multiculturalism that Hall seems to be discussing in this quote.  So, let us look at what the actual quote means.
In the quote, Hall refers to “multi-cultural societies.”  This simply means societies like the US or the UK which contain people from many different cultures.  He says that these societies “throw up” “problems of diversity and multiplicity.”  In other words, multicultural societies have problems that arise because of all the differences within those societies.  “Diversity and multiplicity” simply means that not everyone in these societies is the same.  There are many different cultures within those societies.  This “throws up” problems because people from the different cultures may have trouble accepting one another.  This would not be a problem in a society that was made up only of people from a single culture.
Finally, Hall says that multiculturalism consists of “strategies and policies adopted to govern or manage” these problems.  What he is saying, then, is that multiculturalism is not just the fact that we have multiple cultures in our society.  Instead, multiculturalism is all the things we do to deal with the problems that arise because we have multiple cultures.  Multiculturalism is the set of responses that our government and our society develop to try to address these problems.  Multiculturalism, then, would be things like diversity training for people to learn how not to offend those of other cultures.  It would be rules that allow government documents to be printed in multiple languages.  It is all the things we do to make our multicultural societies work.
So, we can paraphrase Hall and say that multiculturalism is all the things that our government and other parts of our society do to solve the problems that arise because of the fact that we have people from many different cultures within our society.