can someone explain this answer to me? I used modD=MacD x v twice, and got 6.912, which is wrong. help please

Two bonds have the same annual effective yield rate, \\( r \\), where \\( r>0 \\). The bonds have Macaulay duration of 5 years and 6 years with respect to \\( r \\). One of the bonds has modified duration of 5.76 years while the other bond has modified duration of \\( d \\) years. Calculate \\( d \\). (A) 4.760 (B) 4.800 (C) 5.208 (D) 5.240 (E) 6.912 178 375. Solution: B \\( \\bar{v}=\\frac{\\bar{d}}{1+r} \\) \\( 5.76=\\frac{6}{1+r} \\) \\( r=0.041667 \\) \\( \\bar{v}=\\frac{5}{1.041666}=4.8 \\)