Hello
“Work” a stitch or number of stitches just means to follow whatever type of pattern stitch that section would be done in. Sometimes “work” is used rather than saying “knit” as a pattern might not just be knit stitches but a range of stitches to make a rib pattern, a cable or lace pattern etc, or they may be purl stitches, not knit stitches.
Your sweater looks like plain stockinette. To work the stitches on the right side (the outside that we see) you will knit them. To work the stitches on the wrong side (the inside of the sweater) you will purl them.
So, yes, “work” is another way of saying knit, or purl, or follow a set pattern of stitches in the way which has previously been set.
Another example, if you were working 2 x 2 rib, k2, p2 across the row and were told to “work 6” you would look at your next 6 stitches and either knit or purl depending on which type of stitch is needed for each one to keep the rib pattern correct.
Another example often seen is to “work” a given number of rows, again you’d continue the stitch pattern of knits or purls, or cables, or lace, or rib, previously set until the specified number of rows was complete.
This type of instruction often reduces how much has to be said/printed in a pattern.
I hope this helps.