1
Start with rows, columns, or 2Γ3 boxes that already have the most filled cells β they're most constrained.
2
For each empty cell, list which numbers 1β6 are missing from its row, column, and 2Γ3 box. If only one number fits, fill it in.
3
If a number can only go in one cell within a row, column, or box β place it there even if other numbers are also candidates for that cell.
4
Each 2Γ3 box boundary (after rows 2 and 4, and after columns 3) acts like a hard constraint β use it to narrow options quickly.