Let $x$ be the first digit.
Now, according to the question,
The third digit is equal to the first digit.
- third digit $ = $ first digit $= x$
- third digit $ = x$
The second digit is twice the first digit.
- second digit $ = 2 \times$ first digit
- second digit $ = 2x$
The six digit is the sum of the first three digits.
- sixth digit $ = $ first digit $+$ second digit $+$ third digit.
- sixth digit $ = x + 2x + x $
- sixth digit $ = 4x $
The fifth digit is the sum of first two digits.
- fifth digit $ = $ first digit $+$ second digit
- fifth digit $ = x + 2x$
- fifth digit $ = 3x$
The fourth digit is the sum of the fifth and sixth digits.
- fourth digit $=$ fifth digit $+$ sixth digit
- fourth digit $= 3x + 4x $
- fourth digit $ = 7x $
Therefore, the fourth digit will be a multiple of $7.$
The largest possible value of the fourth digit will be $7$ when the value of $x$ will be $1$.
Because if we put $x$ equal to $2$ it will give the two-digit number equal to $\left(7\times 2 = 14\right)$ for the fourth digit, which is not possible.
We can also check for any value of $x.$
$ \therefore $ The largest possible value of the fourth digit $ = 7.$
Correct Answer $:7$
