`Na_(2)B_(4)O_(7)overset(Delta)toNaBO_(2)+B_(2)O_(3)`
`NaBO_(2)+H_(2)O_(2)+H_(2)O to` compound `A(aq)`
The compound `A` the sum of oxidation states of all the oxygen atoms is `X`. Then the value of `(X)` is

Explanation

To solve the problem, we need to determine the sum of the oxidation states of all the oxygen atoms in the compound A formed from the reaction of NaBO2 with H2O2 and H2O. Let's break this down step by step.

### Step 1: Identify the Reaction
The initial reaction is:
\[ \text{Na}_2\text{B}_4\text{O}_7 \overset{\Delta}{\rightarrow} \text{NaBO}_2 + \text{B}_2\text{O}_3 \]

From this reaction, we see that sodium borate (NaBO2) is formed along with boron trioxide (B2O3).

### Step 2: React NaBO2 with H2O2 and H2O
Next, we need to react NaBO2 with H2O2 and H2O:
\[ \text{NaBO}_2 + \text{H}_2\text{O}_2 + \text{H}_2\text{O} \rightarrow \text{Compound A} \]

The product of this reaction is:
\[ \text{Compound A} = \text{Na}_2\text{B(OH)}_4 \cdot 6\text{H}_2\text{O} \]

### Step 3: Determine the Structure of Compound A
The structure of compound A can be represented as:
- It contains boron atoms bonded to hydroxyl groups (OH) and water molecules.

### Step 4: Calculate the Oxidation States of Oxygen
In compound A, we need to calculate the oxidation states of the oxygen atoms. The relevant oxygen atoms are:
1. The oxygen in the hydroxyl groups (OH).
2. The oxygen in the water molecules (H2O).

#### Oxidation State Calculation:
- Each oxygen in the hydroxyl group (OH) has an oxidation state of -1.
- Each oxygen in the water (H2O) also has an oxidation state of -2.

Assuming there are 4 hydroxyl groups and 6 water molecules in the structure:
- For 4 hydroxyl groups: \( 4 \times (-1) = -4 \)
- For 6 water molecules: \( 6 \times (-2) = -12 \)

### Step 5: Sum the Oxidation States
Now we sum the oxidation states of all the oxygen atoms:
\[ \text{Total oxidation state} = -4 + (-12) = -16 \]

### Step 6: Find the Value of X
The problem states that the sum of oxidation states of all the oxygen atoms is \( X \). Therefore:
\[ X = -16 \]

### Step 7: Calculate the Modulus of X
Finally, we need to find the modulus of \( X \):
\[ |X| = |-16| = 16 \]

### Final Answer
Thus, the value of \( (X) \) is:
\[ \boxed{16} \]