Also, in the next sentence, what is buyers commission? Is it referring to the share holder? Or potential share holder? And why does the buyer get commission?
The buyer doesn't get a commission. The buyer pays a commission. So normally a buyer would say, "I want to buy a hundred shares at $20." The broker would then charge the buyer a commission. Assuming 4%, the commission would be
100 * $20 * .04 = $80
So the total cost to the buyer is $2080 and the seller receives $2000. The buyer paid a commission of $80 as the buyer's commission.
In the case of an IPO, the seller often pays the commission. So the buyer might pay $2000 for a hundred shares which have a 7% commission. The brokering agent (or agents may share) pockets a commission of $140. Total paid to the seller is $1860.
Some might argue that the buyer pays either way, as the seller receives money in the transaction. That's a reasonable outlook. A better way to say this might be that typical trades bill the buyer directly for commission while IPO purchases bill the seller. In the typical trade, the buyer negotiates the commission with the broker. In an IPO, the seller does (with the underwriter).
Another issue with an IPO is that there are more parties getting commission than just one. As a general rule, you still call your broker to purchase the stock. The broker still expects a commission. But the IPO underwriter also expects a commission. So the 7% commission might be split between the IPO underwriter (works for the selling company) and the broker (works for the buyer).
The broker has more work to do than normal. They have to put in the buyer's purchase request and manage the price negotiation. In most purchases, you just say something like "I want to offer $20 a share" or "I want to purchase at the market price." In an IPO, they may increase the price, asking for $25 a share. And they may do that multiple times. Your broker has to come back to you each time and get a new authorization at the higher price. And you still might not get the number of shares that you requested.
Beyond all this, you may still be better off buying an IPO than waiting until the next day. Sure, you pay more commission, but you also may be buying at a lower price. If the IPO price is $20 but the price climbs to $30, you would have been better off paying the IPO price even with the higher commission. However, if the IPO price is $20 and the price falls to $19.20, you'd be better off buying at $19.20 after the IPO. Even though in that case, you'd pay the 4% commission on top of the $19.20, so about $19.97.
I think that the overall point of the passage is that the IPO underwriter makes the most money by convincing you to pay as high an IPO price as possible. And once they do that, they're out of the picture. Your broker will still be your broker later. So the IPO underwriter has a lot of incentive to encourage you to participate in the IPO instead of waiting until the next day. The broker doesn't care much either way. They want you to buy and sell something. The IPO or something else. They don't care much as to what.
The underwriter may overprice the stock, as that maximizes their return. If they can convince enough people to overpay, they don't care that the stock falls the day after that. All their marketing effort is to try to achieve that result. They want you to believe that your $20 purchase will go up to $30 the next day. But it might not.
These numbers may not be accurate. Obviously the $20 stock price is made up. But the 4% and 7% numbers may also be inaccurate. Modern online brokers are very competitive and may charge a flat fee rather than a percentage. The book may be giving you older numbers that were correct in 1983 (or whatever year). The buyer's commission could also be lower than 4%, as the seller also may be charged a commission. If each pays 2%, that's about 4% total but split between a buyer's commission and a seller's commission.