Easy enough if it is a "stud" wall but not so simple if it is one of the original brick jobs.
Try an extension cable first ~ they are cheap enough to buy and see if you can place the router somewhere else in the room with improved results.
If you go for the drilling option then you'll need the extension cable anyway.
PS That is a phone extension cable BTW.
PPS I have a number of them spare, I could post you one.