Eqution of 1st circle x²+y2=9, So it'* center is C1u200bu200bu200bu200bu200b->(0,0) and radius r1=3 unit.
Equation of 2nd circle
x²+y2-8x-6y+n2=0
=> (x-4)2+(y-3)2-25+n2=0
So it'* center C2u200bu200bu200bu200bu200b ->(4,3) and radius r2u200bu200bu200bu200bu200b ->(25-n2)^1/2
C1C2=5
C1C2> |r1-r2|
=>5>(25-n2)^1/2
=> |n| < =4
By the given condition n belongs to Z. The possible values of n should satisfy the relation 25-n2>0
=> n = -4,-3,-2,-1,0,+1,+2,+3,+4
So number of possible values of n is 9