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Let the width of the border be x inches.
The total area of the framed picture = Total area of the outer frame - total area of the picture
96 = (10+2x)(6+2x) - 10*6
96 = (20+12x+2x^2) - 60
96 = 20 + 12x + 2x^2 - 60
96 = 2x^2 + 12x - 40
2x^2 + 12x - 136 = 0
x^2 + 6x - 68 = 0
(x+10)(x-4) = 0
x = 4
Therefore, the width of the border is 4 inches.