Work out |-4| + |6| and then |-4 + 6|. Which pair of values is correct, in that order?

Explication

Taking each distance separately adds four to six and gives ten, while combining -4 and 6 first leaves a total two steps from zero, so the bars return two and the two expressions disagree. Assuming they must match treats the bars as though they could be pushed onto each term, which holds only when the terms share a sign.