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The widths are:

b1 = 9 mm

b2 = 5 mm

b3 = 11 mm

b4 = 6.5 mm

My work so far is that the material is FCC, so the allowed HKL planes are all odd and all even. I reasoned that the ratio of the widths are equal to the ratio of the hkl planes magnitude, or w1/w2 = (h1^2+k1^2+l1^2)^.5 / (h2^2+k2^2+l2^2)^.5. When I tried taking the ratios, I couldn't match any of the h^2+k^2+l^2 ratio values to the width ratios for FCC, however, and am unsure of where to go from there.