From a table of \(z\)-values.
\[P(-1.457\le Z\le1.174)=P(Z\le1.174)-P(Z\le-1.457)\]
Referring to this table:
http://facstaff.unca.edu/dohse/Stat225/Images/Table-z.JPG
For this table, the desired probability is given as the area to the left of a certain \(z\)-value. If you're unsure how to use this table, what you do is find the probability/area associated with 1.174 by looking for the area for \(z=1.17\), which gives you 0.879 \(\color{red}{\textbf{(my mistake, sorry!)}}\). And then I'm also getting 0.81 as an answer...
It's interesting that I mistakenly picked the "right" value for \(P(Z\le 1.174)\)... In any case, I think the answer you should be getting might be a typo. Then again, I'm comparing my steps to scribbled notes, so it's possible I've made a mistake somewhere along the line.