Time-shifting operation post the time-reversal operation when performing convolution
Just think of the value of $t$ where $x(0)$ appears. For $x(t+t_0)$ it is at $t=-t_0$, which corresponds to a left shift if $t_0&gt;0$. However, for $x(-t+t_0)$ the value $x(0)$ occurs at $t=t_0$, which is to the right of its original position if $t_0&gt;0$.
You can think of deriving $x(-t+t_0)$ from $x(t)$ in two different ways:

invert the time axis: $x(-t)$
replace $t$ by $t-t_0$, i.e., shift to the right if $t_0&gt;0$: $x(-(t-t_0))=x(-t+t_0)$

Or

shift $x(t)$ to the left (for $t_0&gt;0$): $x(t+t_0)$
invert the time axis: $x(-t+t_0)$: this flips the shifted function from the left to the right of the original function (again, if $t_0&gt;0$).