SQL ANSI JOIN precedence
Logically the joins are resolved in the order of the ON clauses from left to right.

The output of each join is a virtual table that goes into the next join.

So for the query in your question the virtual table result of A LJ B is then right joined onto C. The join condition of B.Col3 = C.Col4 will lose any null extended rows preserved by the original left join effectively turning the first join back into a inner join and the resulting virtual table (which preserves all rows from C) is then inner joined onto D.

So your initial query can be simplified as 

SELECT *
FROM TBLA A
INNER JOIN TBLB B ON A.Col1 = B.Col2
RIGHT JOIN TBLC C ON B.Col3 = C.Col4
      JOIN TBLD D ON C.Col5 = D.Col6


Which is effectively the same as (A IJ B) ROJ (C IJ D)  

The order of the ON clauses is not necessarily the same as the order the tables appear in the query. This could also be rewritten as (C IJ D) LOJ (A IJ B)

SELECT *
FROM   TBLC C
       INNER JOIN TBLD D
         ON C.Col5 = D.Col6
       LEFT JOIN TBLA A
                 INNER JOIN TBLB B
                   ON A.Col1 = B.Col2
         ON B.Col3 = C.Col4 


The position of the on clauses means that the outer join is carried out between the two virtual tables resulting from  (C IJ D) and (A IJ B) rather than just on a single table.

In your second query conceptually the virtual table A x C is left joined onto B preserving the entire cartesian product then the result of that is joined onto D with the predicate C.Col5 = D.Col6. This eliminates any rows from the final result that do not inner join between C and D meaning it is equivalent to 

SELECT *
FROM   TBLC C
       JOIN TBLD D
         ON C.Col5 = D.Col6
       CROSS JOIN TBLA A
       LEFT JOIN TBLB B
         ON A.Col1 = B.Col2
            AND B.Col3 = C.Col4