How do managers coordinate the employees contribution towards the
achievement of organisational goals of government organisations?

Interesting question, but not a $5 question.  You will need
to recognize that the government and organizations within
it, at federal, state and local levels will have a multitude of
objectives and goals.  In some cases, they will be measured
against hard metrics like completing tasks, serving customers
or maintaining 'stuff' without a defined budget.  In other cases
they will be measured on saving money or justifying money
against other priorities.  Most organizations try/claim to have
objectives and publicize them and their performance.  The
paradox with government is the best way to get more money
the next year is to use all of what you have this year to justify
it.  This is simplistic and a common joke, but this is one of
the reasons that performance and savings are not encouraged
in many cases - you are not rewarded for doing either and
your life becomes increasingly difficult.  Surprisingly enough,
many Government organizations are sophisticated in their
measurement and performance, some even go overboard.
Good luck on getting an answer, and it would take significant
resources for a researcher to provide examples covering the
spectrum of different methods of doing this just in the U.S..

Again, you might want to review the pricing
policy for GA to get a better idea on what
you can get for your investment.  Good luck
on your project, and if you narrowed down
this to something like:

"Where can I get an example of metrics
government (or 1, 2 or 3) organizations use
to measure themselves?"

You might get a better answer then mine.
Good luck.