To find dimensions of any physical quantity, consider its definition or a formula that connects this quantity to the ones with the known dimensions.
Work, by definition, is the scalar product of the force acting on the object and its displacement. (The displacement might or might not be due just to this particular force.)
`W = vecF*Delta vecx`
This can also be written as
`W = F*|Deltavecx|*cos(theta)` , where `theta` is the angle between the force vector and the displacement vector.
The cosine of an angle is dimensionless. The displacement has the dimensions of length, [L], or meters.
The force is measured in Newtons, which is a unit composed of other fundamental units:
`1 N= kg*m/s^2`
The dimension of force is `[F] = [M]*[[L]]/[T]^2`
Thus, dimension of work is
`[W]=[M]*[[L]]/[T]^2*[L] = [M]*[L]^2/[T]^2` .
In the metric system, work is measured in Joules:
`1 J = N*m = kg*m^2/s^2` .
Hope this helps.