To solve this equation, we can use the formula for the sum of an arithmetic series.

The sum of an arithmetic series is given by the formula: S = (n/2)(2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.

In this case, the first term is x, the common difference is 2, and the sum is 1392. We need to find the value of x.

Let's substitute these values into the formula:

1392 = (n/2)(2x + (n-1)2)

Simplifying the equation:

1392 = (n/2)(2x + 2n - 2)

Dividing both sides by 2:

696 = n(x + n - 1)

Now, we need to find the values of n and x that satisfy this equation.

Since we have an equation with two variables, we need another equation to solve for both variables. We can use the fact that the last term in the series is x + 46.

The last term is given by the formula: a + (n-1)d

In this case, a = x and d = 2. So, the last term is x + (n-1)2.

We know that the last term is x + 46, so we can write the equation:

x + (n-1)2 = x + 46

Simplifying the equation:

(n-1)2 = 46

Dividing both sides by 2:

n - 1 = 23

Adding 1 to both sides:

n = 24

Now, we can substitute this value of n back into the first equation:

696 = 24(x + 24 - 1)

Simplifying the equation:

696 = 24(x + 23)

Dividing both sides by 24:

29 = x + 23

Subtracting 23 from both sides:

x = 6

Therefore, the value of x is 6.