Could it have been a ‘cadet’ edition? These are listed on the Hornblower page of Wikipedia
Four "Cadet Editions" were released by Little Brown and later by Michael Joseph, each collecting two Hornblower novels and edited for younger readers: Hornblower Goes to Sea (1953, 1954), from Mr. Midshipman Hornblower and Lieutenant Hornblower; Hornblower Takes Command (1953, 1954), from Hornblower and The Atropos and Beat To Quarters; Hornblower in Captivity (1939, 1955), from A Ship of the Line and Flying Colours; and Hornblower's Triumph (1946, 1955), from Commodore Hornblower and Lord Hornblower.
Failing that, there is this edition:
Reader's Digest Best Loved Books For Young Readers: Vol. 3: Captain Horatio Hornblower; Jane Eyre; My Friend Flicka; Alone
Per Wikipedia again
The first three novels written, The Happy Return, A Ship of the Line, and Flying Colours were collected as Captain Horatio Hornblower (1939) by Little Brown in the US
NB. Beat to Quarters is the US title for The Happy Return.
I have found an eBay listing for the RD edition, with an incomplete photograph of the copyright page, which includes
Beat to Quarters, copyright 1937, (c) 1965, by Cecil...(text runs out of image)
is part of the trilogy Captain Horatio Hornblower, published at $5 by Little, Brown & Co.