Solution:-

From the given figure, CD || LA and DE || AC,

Consider the ∆BCA,

BE/BC = BD/BA

By using the corollary of basic proportionality theorem,

BE/(BE + EC) = BD/AB

4/(4 + 2) = BD/AB … [equation (i)]

Then, consider the ∆BLA

BC/BL = BD/AB

By using the corollary of basic proportionality theorem,

6/(6 + CL) = BD/AB … [equation (ii)]

Now, combining the equation (i) and equation (ii), we get

6/(6 + CL) = 4/6

By cross multiplication we get,

6 x 6 = 4 x (6 + CL)

24 + 4CL = 36

4CL = 36 – 24

CL = 12/4

CL = 3 cm

Therefore, the length of CL is 3 cm.