Can someone explain to me how to calculate the following:

| -3 - | -7-7||.

The '|' signs are absolute value - the results are always positive.

Calculate the inner '|' first, as you would parentheses.

|-3-|-7-7||
= |-3-|-14||
= |-3-14| because |-14| = the absolute value of -14 = 14
= |-17|
= 17