For a 4x4 grid this are the values 1 - 4.
While doing this keep these rules in mind:
A value can only appear once in a row/column.
If there are markers between the cells then the rule between these cells must be valid as bigger or smaller than.
Each row/column is unique and must not appear more than once.
Below is an example of a puzzle and the required steps and logic to complete it.
Descriptions:
Green colored values are cell references
Cyan colored values are given at the start
Red colored values are the step numbers
White colored values are the step values

1. B2-B4 3 cells with > markers inbetween...
Only valid options: 1-2-3, 1-2-4, 1-3-4, 2-3-4
B4 already contains 4 so only 1-2-3 is possible
2. Complete row B with 4 in B1
3. Row A has 1 (A1) so only 2 is valid in A4
4. Complete the column with 1 (C4)
5. Only 1 can be at D3 as 4 is in D4 already
6. Complete column 3 with 4 (A3)
7. Complete row A with 3 (A2)
8. D1 is 3 as other rows/cols have 3 already
9. Complete column 1 with 2 (C1)
10. Complete row C with 4 (C2)
11. Complete row D with 2 (D2)
Completed!
Good luck on solving the puzzles!