Select the correct indirect form of the given sentence. I said to my…

The correct answer is Option (4) → I told my mother that I would certainly take her to Bangalore that week.

Reporting your own promise:

Change	Direct	Indirect	Why
Reporting verb	said to my mother	told my mother	A listener is named. So "said to" becomes "told".
Joining word	" " (quotation marks)	that	The reported statement is joined with "that".
Pronoun change	you	her	I was speaking to my mother, so "you" becomes "her". "I" stays "I", as I am reporting my own words.
Tense change	will	would	"Will" changes to "would" (would + base form (V1)) after the past "said".
Time and place words	this week	that week	The report comes later. So "this" changes to "that".
Full sentence	I said to my mother, "I will certainly take you to Bangalore this week."	I told my mother that I would certainly take her to Bangalore that week.

Other time words change the same way: today → that day, now → then, tonight → that night. Example: Gopal said, "I will finish it today." → Gopal said that he would finish it that day.

Why the Other Options are Incorrect?

Option 1: I told my mother that she would certainly take her to Bangalore that week. — Incorrect. The promise is mine. "She would take" wrongly makes the mother the one who takes.

Option 2: I told my mother he would certainly take her to Bangalore that week. — Incorrect. "He" brings in some other person. The one who will take her is "I".

Option 3: I told my mother that I would certainly take her to Bangalore this week. — Incorrect. "This week" is not changed. In the report it becomes "that week".