In terms of British currency, a sixpence (no longer minted in the U.K.) is worth less than a shilling. The eNotes source states that...
The shilling is worth more than a pence. Prior to the change in currency in 1971, the shilling was worth 12 old pence. And another source notes that sixpence is approximately six "pennies."
Harold's father asks his son:
You know, I've been thinking about you -- and you look worried. Haven't lost sixpence and found a shilling have you, because I wouldn't mind doing that?
To find some meaning in this, it's important to look at it in the context of the story as a whole. Harold's father (called "the father") has just lost his business. Harold enters, purposefully, to offer "moral support" for his father. When the father makes note of the pence and shilling, it reflects his preoccupation with money. I believe he is inferring that the son's worry could be over losing a small amount of money only to find a greater amount. There could be the presence of some old superstition about "found money," or "getting back more than what was lost," perhaps a sign of bad luck. Some people believe strongly in a universal balance—that getting more than he had lost might mean there is trouble to come.
It is not surprising to note that the father would welcome extra money under any circumstance because money is so tight. Whereas the father asks Harold if he is worried about something, the old man becomes irritated when Harold wonders if his father is worried.
Worrying? You keep on using that word. I'm not worrying. Things are fine...
This supports what we already know from our reading: that the father does not have much of a regard for his son, and the very fact that he is nice to him at all—now—is out of character for the older man. They go on, Harold trying his best not to annoy his father, and at last "the old man" states:
Money...isn't necessary at all.
This is a complete reversal from the tone of his father's original comment. Where he had wished to find some extra money at the beginning of the conversation, now he says it's meaningless.
As they have been talking, the reader has gotten the impression that the father has two faces: one is small and diminished by his loss of the business—this is the face probably responsible for being nicer to Harold than usual. The other is a bigger, more powerful face. It is probably the one that was overbearing and unkind with Harold when the father was at the "top of his game." Harold imagines that the two "faces" are struggling for dominance. It seems as if the pushy man Harold has tried to tolerate for so long is disappearing as his sense of self-importance diminishes with his dwindling bank account.
Harold finally tells his father that he wishes he could help his dad financially; he can't, but if he had the means, he would try to raise money for the older man. The only thing the man hears is "raise money"—nothing else. Money, it seems, is still dominant.
"Raise it?" said the old man sharply. "Why didn't you tell me before you could raise money? How can you raise it? Where? By when?"
The father's original comment about the pence and shilling seems to reflect his concern about money; his wishing that he had extra cash foreshadows the father's inability to let his former life go, though he tries hard to convince Harold of the opposite.