Which of the following inequalities is equivalent to 10 – 2x > 18?

You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide by a negative number, the sign of the inequality flips.

To illustrate,

10 – 2x > 18
10 > 18 + 2x (Correct)
10 - 18 > 2x (Correct)
-8/2 > x (Correct. You are dividing by 2, which is positive so no changes)
-4 > x or x < -4 (Correct)

On the other hand,
10 – 2x > 18
-2x > 18 - 10 (Correct)
x > 8/(-2) (Incorrect. When you divide by -2, the sign of the inequality flips so x < 8/(-2))

So inequality differs from equation in that you cannot divide/multiply an inequality by x if you do not know the sign of x. If x is positive, the inequality remains the same. If x is negative, it flips.)