the number of number pairs (x,y) which will satisfy the equation x2-xy+y2=4(x+y-4)

x²-xy+y²=4(x+y-4)

  x²-x(y+4)+y² -4y +16=0

if it has real solution then D≥0

so (y+4)² -4( y² -4y +16)≥0

 or (y-4)²  ≤0

 only possible when y=4

so for y=4 only one value of x=4 possible

so only one pair (4,4) is the solution

Hope it helps

Regards

Arun (askIITians forum expert)