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The value of $x$ in the equation $4x - 2 = 10$ is $3$.

To determine the value of $x$, we will solve the equation step by step. The given equation is

Our objective is to isolate $x$ on one side of the equation.

First, we eliminate the constant term on the left side by adding $2$ to both sides:

This simplifies to

Next, we need to isolate $x$ by removing the coefficient $4$. We achieve this by dividing both sides of the equation by $4$:

This simplifies to

Thus, the value of $x$ is $3$. To verify our solution, we can substitute $x$ back into the original equation and check for equality.

Substituting $x = 3$ into the original equation gives:

This simplifies to

which further simplifies to

Since both sides of the equation are equal, our solution is confirmed to be correct. Therefore, the value of $x$ that satisfies the equation $4x - 2 = 10$ is indeed $3$.