The number of particles crossing unit area perpendicular to x-axis in unit time is given by $\mathrm{n}=\frac{-\mathrm{D}\left({\mathrm{n}}_2-{\mathrm{n}}_1\right)}{{\mathrm{x}}_2-{\mathrm{x}}_1}$  where n₁ and n₂ are number of particles per unit volume for the value of x meant to x₁ and x₂. The dimensions of D are

$\mathrm{n}=\frac{-\mathrm{D}\left({\mathrm{n}}_2-{\mathrm{n}}_1\right)}{{\mathrm{x}}_2-{\mathrm{x}}_1}$

here n is the no of particles crossing per unit area per unit time so dimensionally L^-2T^-1 . n₂ and n₁ are no of particles per unit volume have dimension L^-3. x₁ and x₂ are the distance have dimension L

Equating the dimension on both sides

 L^-2T^-1=D (L^-3/L)

[D]=M⁰L²T^-1