$\text{a)}\left|10-\left(-10\right)\right|=\left|10+10\right|=\left|20\right|=20$     

$\text{b)}\left|-1+4\right|=\left|3\right|=3$  

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

$\text{d)}\left|19-6\right|=\left|13\right|=13$