In ΔADE and ΔABC

∠ADE = ∠ABC [Corresponding angles as DE || BC]

∠AED = ∠ACB [Corresponding angles as DE || BC]

ΔADE ~ ΔABC [By Angle-Angle Similarity criterion]

[Corresponding sides of similar triangles are in the same ratio]

Now,

Given, AD = 3 cm

DB = 2 cm

DE = 6 cm

⇒ AB = AD + DB = 3 + 2 = 5 cm

Using this in above equation,

⇒ BC = 10 cm