Ok, cool.
So let me give you some more information.
That LM1875 is a class AB audio amplifier chip, which means it's kind of inefficient and therefore will produce A LOT of heat. It MUST be connected to a big heatsink. If you want to get 20 watts per channel, you're going to need a CPU style heatsink with a fan.
Here's the datasheet for this chip :
http://www.ti.com/lit/ds/snas524a/snas524a.pdfLook at page 4, figure 5:
This tells you that with a 8 ohm speaker, the amplifier can function with as little as +/- 10v (the x axis), but the maximum output power will only be around 5w (the y axis). Following the line, you can see it does ~10w at +/-15v, a bit more than 15w at +/- 20v and nearly 25w at +/-25v.
With 4 ohm speakers, the output power will be slightly higher.
So what you need to get from this is that you don't necessarily need two 24v power supplies, especially if you don't have 15-20w speakers.
On the same page, you have figure 8 : Device Dissipation vs Ambient Temperature and this picture must be used together with Figures 9 and 10 on the next page
So let's say you want to power with +/- 24v ... we'll look on the +/- 25v curves.
If you have a 4 ohm speaker, you'll look in the Figure 9 chart - you can see that to produce 15w of audio power, there's gonna be a bit over 30 watts of heat produced.
If you go with 8 ohm speaker, you'll look in the Figure 10 chart - you can see that to produce 15w of audio power, there's gonna be nearly 20 watts of heat produced.
This heat (20..30w) must be dissipated safely... and that's what Figure 8 shows you.
For safety, assume the ambient temperature (the temperature of the box where the amplifier will be) will go up to 40 degree Celsius, so you go on the x axis at 40 degrees C and then you go up.
You can see that the bottom two heatsinks (rated for 10c/w or 5c/w) are not good enough.
The next curve shows a heatsink rated for 2c/w and it's just barely good enough if you'll do 15w of audio power with 8 ohm speaker (which dissipates nearly 20w)
To safely dissipate the 30w of heat you'd produce to get 15w of audio with 4 ohm speaker, you can't even use a 1c/w heatsink on all its own - you'll need to supplement it with a fan to blow air over it and help cool it.
As an idea, this is the kind of heatsinks you'd need for 10w+ of heat dissipation :
https://www.digikey.com/short/p2mv1qThe link above shows heatsinks with < 3c/w natural convection (<1..2c/w with fans)
So my advice would be to first decide on the speakers you're gonna use, and ideally use 8 ohm speakers as these amplifiers will dissipate less heat with such speakers.
If you're gonna have a couple of 5w or 10w speakers, there's no point to power this amplifier with +/- 24v, because you can produce 10w with just +/- 15v, and you're gonna produce less heat.
Making a power supply using a transformer is very easy, here's a schematic :
The unlabeled resistors should be something around 4.7kOhm - 10 kOhm and rated for 1w ... basically, they're there to discharge the big capacitors when the amplifier is not in use.
The bridge rectifiers should be something like 6A or higher... they're very cheap...here's a 8A one for 1.25$ :
https://www.digikey.com/product-detail/en/micro-commercial-co/GBJ806-BP/GBJ806-BPMS-ND/8554715So let's say you decide you want 15w of audio power and you have 8 ohm speakers. In that case, +/-20v is gonna be enough but we can go with +/- 25v curves.
Looking at Figure 10 chart, at 15w of audio, the +/-25v curve tells you there's gonna be nearly 20w of heat produced. So, in total, the audio amplifier needs 15w audio + 20w heat = 35w of power to achieve what you want.
For stereo sound, you'll need double this, plus some reserves... so you need something that can give you minimum 70w...
Now you can go look for a transformer with either two secondary windings or center tap, which outputs 15v AC or more on each secondary winding, or 30-36v AC if transformer has a single secondary winding with center tap
Here's some examples with center tap
21$ : 28v AC 100w :
https://www.digikey.com/product-detail/en/triad-magnetics/F8-28/237-1722-ND/487865121$ : 36v AC 100w :
https://www.digikey.com/product-detail/en/triad-magnetics/F8-36/237-1723-ND/487865232$ (with wires) 35v AC 140w :
https://www.digikey.com/product-detail/en/triad-magnetics/F-191U/F-191U-ND/7318079With dual secondary windings :
21.4$ 2 x 12v 80w :
https://www.digikey.com/product-detail/en/triad-magnetics/VPS24-3300/237-1276-ND/66616221.4$ 2 x 14v 80w :
https://www.digikey.com/product-detail/en/triad-magnetics/VPS28-2800/237-1280-ND/66616621.4$ 2 x 18v 80w :
https://www.digikey.com/product-detail/en/triad-magnetics/VPS36-2200/237-1285-ND/66617128$ 130w
2x12
https://www.digikey.com/product-detail/en/triad-magnetics/VPS24-5400/237-1277-ND/6661632x14
https://www.digikey.com/product-detail/en/triad-magnetics/VPS28-4600/237-1281-ND/6661672x18
https://www.digikey.com/product-detail/en/triad-magnetics/VPS36-3600/237-1286-ND/66617236$ 175w
2x12
https://www.digikey.com/product-detail/en/triad-magnetics/VPS24-7300/237-1278-ND/6661642x14
https://www.digikey.com/product-detail/en/triad-magnetics/VPS28-6250/237-1282-ND/6661682x18
https://www.digikey.com/product-detail/en/triad-magnetics/VPS36-4800/237-1287-ND/666173