$\text{a)}\left|-5\right|=5$  

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$\text{b)}\left|-2+12\right|=\left|10\right|=10$  

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$\text{c)}\left|-2\right|+\left|2\right|=2+2=4$  

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$\text{d)}-\left|-3\right|+\left|-3\right|=-3+3=0$  

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$\text{e)}\left|\sqrt{3}-2\right|=2-\sqrt{3}$  

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$\text{f)}\left|\frac{1}{2}-\frac{\sqrt{2}}{2}\right|=\frac{\sqrt{2}}{2}-\frac{1}{2}$