In $$\triangle$$ABC, E and D are points on sides AB and AC, respectively, such that $$\angle$$ABC = $$\angle$$ADE. If AE = 6 cm, AD = 4 cm

and EB = 4 cm, then the length of DC is:

In $$\triangle$$ABC and $$\triangle$$ADE,

$$\angle$$ABC = $$\angle$$ADE

$$\angle$$BAC = $$\angle$$DAE

So $$\triangle$$ABC is similar to $$\triangle$$ADE

$$\Rightarrow$$  $$\frac{AB}{AC}=\frac{AD}{AE}$$

$$\Rightarrow$$  $$\frac{AE+EB}{AD+DC}=\frac{AD}{AE}$$

$$\Rightarrow$$  $$\frac{6+4}{4+DC}=\frac{4}{6}$$

$$\Rightarrow$$  $$\frac{10}{4+DC}=\frac{2}{3}$$

$$\Rightarrow$$  4 + DC = 15

$$\Rightarrow$$  DC = 11 cm

Hence, the correct answer is Option D