The length of AB is 12 cm.Step-by-step explanation:Given data:∠ACB = ∠CDAAC = 6 cmAD = 3 cmTo find: Length of ABFrom the figure attached below, in ∆ ABC & ∆ ACD, we have∠A = ∠A ….. [∵ common angle for both the triangle]∠ACB = ∠CDA ….. [∵ given]∴ By AA similarity, ∆ABC ~ ∆ACDSince the sides of two similar triangles are proportional to each other∴ \\frac{AB}{AC} = \\frac{AC}{AD} = \\frac{BC}{CD}Now taking,\\frac{AB}{AC} = \\frac{AC}{AD}⇒ AC² = AB * AD⇒ 6² = AB * 3 …… [given AC = 6 cm & AD = 3 cm]⇒ 36 = AB * 3⇒ AB = 36/3 = 12 cm