Let's solve this problem step by step. We are given that a flagstaff stands on the top of a vertical tower and a man standing 60 m away from the tower observes that the angles of elevation of the top and bottom of the flagstaff are 64° and 62° respectively. We are asked to find the length of the flagstaff.

Let's call the height of the tower `h1` and the length of the flagstaff `h2`. Using the tangent function, we can write two equations for `h1` and `h2`:

tan(62°) = h1 / 60

h1 = 60 * tan(62°)

tan(64°) = (h1 + h2) / 60

h2 = 60 * tan(64°) - h1

Substituting the value of `h1` into the second equation, we get:

h2 = 60 * tan(64°) - 60 * tan(62°)

h2 = 60 * (tan(64°) - tan(62°))

So, the length of the flagstaff is **60 * (tan(64°) - tan(62°))**.