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Why does the voltmeter shows negative reading when connected in reverse order? What does it mean by negative voltage? Should we say voltage drop across $R2$ is $+12V$ or $-12V$? How to apply Kirchoff's Voltage Law in such cases?

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The $+$ and $-$ signs of the voltmeter means that the reading on the meter is the potential of the terminal labelled $+$ relative to the terminal labelled $-$.

So for the top voltmeter the potential of the $+$ terminal is $8.00\,\rm V$ higher than the $-$ terminal and for the right hand voltmeter the potential of the $+$ terminal is $12.00\,\rm V$ lower than the $-$ terminal.

Starting at the bottom right hand corner and moving counter-clockwise,
going through resistor $R2$ the potential rises by $12\,\rm V$,
going through resistor $R1$ the potential rises by $12\,\rm V$, and
going through battery $BAT1$ the potential falls by $20\,\rm V$
resulting in a total potential change of $+12+8+(-20) = 0\,\rm V$ when going arond a complete loop as predicted by Kirchhoff's voltage law.

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It means the positive terminal of the meter is at a lower potential than the negative terminal.

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