Hey there, welcome to the forums!

Consider what happens when you take each transformation in order.

First, we want to dilate horizontally by a factor of 2 ie. we transform \(\sin^{-1}(x-4) \text { to } \sin^{-1}\left(\frac{x-8}{2}\right)\).

Then, we shift the graph right by 1. Note that this actually means we replace \(x\) with \(x-1\), we don't subtract 1 from the entire expression. The latter is especially problematic as in this case, subtracting 1 from the whole expression actually implies that shifting was done prior to dilation - which is not the case It's important to be careful here, and in any other question that involves this.

Hence, we take the transformation from \(\sin^{-1}\left(\frac{x-8}{2}\right) \text{ to } \sin^{-1}\left(\frac{(x-1)-8}{2}\right)\), which gives you the correct answer.

Hope this helps