"Question 6c, practice problem 3, is the lastrow operation be like this and rank will be 4 instead?"

Your row reduction is correct but you just need to interpret correctly.

The definition of a pivot is the leading entry on a row.

A pivot column is a column containing a pivot.

Pivot columns are linearly independent but not the other ones.

So there are 3 pivots >>> 3 pivot columns >>> 3 linearly independent columns >>> rank is 3.

Don't forget that as a check the dimension of the row space should be the same as the dimension of the column space - that's the definition of rank.

So since there are 3 linearly independent rows (easy to see) then it makes sense that only 3 columns are linearly independent.

In fact you can see that actually the 2nd and 4th columns are exactly the same as each other so they are definitely linearly dependent.