Solution:-

From the figure,

PQ || AC, AP = 4 cm, PB = 6 cm and BC = 8 cm

∠BQP = ∠BCA … [because alternate angles are equal]

Also, ∠B = ∠B … [common for both the triangles]

Therefore, ∆ABC ~ ∆BPQ

Then, BQ/BC = BP/AB = PQ/AC

BQ/BC = 6/(6 + 4) = PQ/AC

BQ/BC = 6/10 = PQ/AC

BQ/8 = 6/10 = PQ/AC … [because BC = 8 cm given]

Now, BQ/8 = 6/10

BQ = (6/10) ×8

BQ = 48/10

BQ = 4.8 cm

Also, CQ = BC – BQ

CQ = (8 – 4.8) cm

CQ = 3.2cm

Therefore, CQ = 3.2 cm and BQ = 4.8 cm