\( x = \square + 2 ( x + 4 ) - 10 = x + 6 \)

We start with the equation written as \[ x = \square + 2(x+4)-10 = x+6. \] Because the expression in the middle is set equal to both \(x\) (on the left) and \(x+6\) (on the right), every pair of these expressions must be equal. In particular, we require that \[ \square + 2(x+4)-10 = x+6. \] Step 1. Expand and simplify the left‐side expression: \[ \square + 2(x+4)-10 = \square + 2x+8-10 = \square + 2x-2. \] Step 2. Set the simplified expression equal to the right‐hand side: \[ \square + 2x-2 = x+6. \] Step 3. Solve for \(x\) in terms of the unknown number (represented by the square, \(\square\)). First, subtract \(x\) from both sides: \[ \square + 2x-2-x = x+6-x \quad\Longrightarrow\quad \square + x-2 = 6. \] Then, add 2 to both sides: \[ \square + x = 8. \] Finally, solve for \(x\): \[ x = 8 - \square. \] Step 4. Now, recall that the very first part of the equation reads \[ x = \square + 2(x+4)-10, \] and the last part of the equation reads \[ x = x+6. \] The equation \[ x = x+6 \] implies \[ 0=6, \] which is a contradiction. Because the equality \(x = x+6\) cannot hold for any real number \(x\), the whole chain of equalities \[ x = \square + 2(x+4)-10 = x+6 \] is inconsistent. In other words, there is no real value of \(x\) (nor any choice for the number in the square) that makes the given equation true. Thus, the equation has no solution.