Think back to the definition of absolute value:
• If <em>x</em> ≥ 0, then |<em>x</em>| = <em>x</em>.
• If <em>x</em> < 0, then |<em>x</em>| = -<em>x</em>.
In other words, the absolute value always returns a positive number. So if <em>x</em> is positive, leave it alone; but if it's negative, then you have to negate it to get a positive number back.
This means that you cannot simply reduce |<em>x</em> - <em>y </em>| to <em>x</em> - <em>y</em> because you need to consider the possibility that <em>x</em> - <em>y</em> may be negative, in which case |<em>x</em> - <em>y</em> | would reduce to -(<em>x</em> - <em>y</em>) = <em>y</em> - <em>x</em>.
In this case,
|4√2 - 6| = -(4√2 - 6) = 6 - 4√2
because 4√2 < 6, which you can determine by comparing both of these numbers as square roots:
4√2 = √16 √2 = √32
6 = √36
and √32 < √36 because 32 < 36.
Similarly,
|2√10 - 6| = 2√10 - 6
because
2√10 = √4 √10 = √40
6 = √36
So ultimately,
|4√2 - 6| + |2√10 - 6| = (6 - 4√2) + (2√10 - 6) = 2√10 - 4√2