As Wikipedia says, James Annesley (1715–60) "was an Irishman with a claim to the title Earl of Anglesey, one of the wealthiest estates in Ireland. The dispute between Annesley and his uncle Richard Annesley was infamous in its time, but his story is perhaps best known today as a possible inspiration for the 19th century novel Kidnapped by Robert Louis Stevenson, among other works of literature"—later mentioning "Eliza Haywood's novel Memoirs of an Unfortunate Young Nobleman (1743) … [which] narrates a wildly inaccurate imagining of James' life in the American Colonies." I'd dispute the "wildly inaccurate" but two contributors to this Wikipedia entry are engaged in a war and I have no desire to get involved!
Anyway, I know of three engravings of James Annesley, all appear to be based on one (above), published in March 1744, attributed to George Bickham the Younger (1706–71; fl.1736–58), after an original by Kings—possibly Giles King (fl.1732–46). Two of the three appear on eighteenth-century editions of The trial … between Campbell Craig, Lessee, of James Annesley, plaintif, and the Right Honourable Richard Earl of Anglesey, Defendant which I have. There were many, competing, editions of this trial, the two illustrated editions (below) being that printed "for R. Walker" (ESTC: n13750; online here) and "for Jacob Robinson" (ESTC: t195578).
As you can see below, by comparing each of the reprints with the original, the Walker plate is reversed. The ship, on the left of the original, is now on the right (below); and Annesley, who is facing left is now facing right. I flipped and paired the portraits below to show the background in the same position in both plates, reversing details on Annesley.
Although major features are flipped, minor ones are not, so that, when reversed like this, they do not match: note, in particular, that his buttons and button-holes are now on the reverse side. This is because, if the copiest had copied these features along with the others, in reverse, they would appear be on the wrong side according to prevailing fashions: men's buttons always being on their right, or the viewer's left!
With the Robinson plate (below), the background has simply been erased, so no reversal of major and minor features is necessary. Note how the features of the original ornate frame are retained, and the crown, though the frame is at odds with such an austere background.