According to the question it is given that,

Inner radius of the well $=4m$

Depth of the well $=14m$

As we know that,

Formula for Volume of the cylinder $=\pi {{r}^{2}}h$

$=\pi \times {{4}^{2}}\times 14$ …. (i)

From the question it is given,

The earth taken out from the well is evenly spread all around it to form an embankment

And, the width of the embankment $=3m$

Therefore, the outer radius of the well $=3+4m=7m$

Formula for volume of the hollow embankment $=\pi \left( {{R}^{2}}-{{r}^{2}} \right)\times h$

$=\pi \times \left( {{7}^{2}}-{{4}^{2}} \right)\times h$ …… (ii)

On equating both the equations (i) and (ii), we get

$=\pi \times {{4}^{2}}\times 14=\pi \times \left( {{7}^{2}}-{{4}^{2}} \right)\times h$

$h={{4}^{2}}\times 14/\left( 33 \right)$

$h=6.78m$

Therefore, the height of the embankment so formed is $6.78m$.