Question

why do you think holmes asks watson to examine the stick​

Answer 1

Holmes knows what Watson has in his hands because he can see his reflection in the coffee-pot. He asks what Watson can tell him about Mortimer by examining his stick.

Answer 2

The story starts with Holmes and Watson in their house at 221b street.

We see that Holmes was sitting by keep his back towards Watson.

He asks Watson what he makes of the stick as Watson is an astute observer.

By observing the stick carefully, He concludes that,

The sticker belongs to James Mortimer.

He might be an elderly doctor who was gifted this stick.

Then Sherlock praises him and takes the stick by himself.