Linear density is the number of lattice points or repeat distances per unit length in a particular direction. Since aluminum is FCC, along the  direction (face diagonal in the top plane) there are two lattice points (atoms, not counting the starting point) encountered. (see Figure 3-13, page 52).
The distance (see packing factor) is . Since the lattice parameter is 4.04958 Angstroms, I write:
The units for this value are lattice points per Angstrom. Changing to nanometers, it becomes 3.49 lattice points per nm.