Can lights spread a cone out that is equal in diameter to the height
that the can is above the floor. So a light that is 8 feet above the
floor will spread a cone out in an 8 foot diameter circle. That is not
to say that a room that is 8' x 8'only needs one can on an 8' foot
ceiling as the brightness of that cone diminishes as it spreads. You
also want to have the cones overlap to maximize efficiency of the
lighting. The lights need to be placed above the counter so as not to
cause any shadows from people standing at the counter or from wall
cabinets. The drawing that you posted is hard to read the dimensions as it does not enlarge well but using the sink as a nominal scale I am estimating 10 total. 8 along the "L' run of cabinets and 2 in front of the cabinets on the side. I would have one switch to control them at each entrance to the kitchen with the side 2 cans switched separately if that is a buffet type of cabinet

Great advice. Also consider a dimmer switch and using the newer warm LED bulbs, crazy expensive in the short run...worth it in the long term.