The inequality given is:

$-6 > -x + 3$

To solve for $x$, follow these steps:

1. Subtract 3 from both sides to isolate the term involving $x$ on the right-hand side: $-6 - 3 > -x$ This simplifies to: $-9 > -x$

2. Now, to solve for $x$, multiply both sides of the inequality by $-1$. Remember that when multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality sign