Which linux best for dual core processor

I have Dell Optiplex dual core 4GB Ram ,250GB HDD so which best for old machines

Hello @SUKHOI35MKI,
Welcome to the Linux.org forum, enjoy!
My best advise is to try several live usb distros. Stick to the lighter ones XFCE, AntiX, MX, Puppy Are all good to try Puppy would run nicely on that machine. But it's non standard in many ways. This page may lead to one that will suit your needs.

16 Best Lightweight Linux Distributions for Older Computers

Don’t throw your old computer just yet. Use a lightweight Linux distro and revive that decades-old system.

itsfoss.com

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But in the end only you can choose which is best for you. If it's a 32 bit processor that will limit your choices also.

Lubuntu, Xubuntu, Antix, Arch and LMDE (my personal choice for these configurations)

Welcome

Your choice is not only determined by how many cores your CPU has, but how old is the CPU and how much ram do you have, examples a 2008 machine with a duo E series CPU would be best suited to lightweight distros whereas a 2009 machine with a T series duo core [or newer] will run any distribution , provided you have a min 4 gb of ram [my own laptop is a 2010 T series with 4 gb ram and I run Mint LMDE6 on it without problems, my only concession was to swap out the old plate spinner Hard-drive for an ssd, as it increases the read/write speeds some 10-fold.

I'm personally a fan of the XFCE Desktop Environment, so Xubuntu or Mint XFCE are my top recommendations.

Freepoorman said:

I'm personally a fan of the XFCE Desktop Environment

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This is one of the beauties of Linux, it is YOUR choice, minimal, hacking tosh, broken windows, plasma, [add infinitum], with a choice of so many desktop environments and their variants, everyone can choose what they like best, and if that is not good enough you can cut slash and add to personalise further if they want,
Linux can be summed up in one word "CHOICE"

After testing LMDE6 and MX Linux version 23 on my 11 year old Sony laptop I'm well pleased.

Giving them a go should prove well I'd say:-

kc1di said:

Stick to the lighter ones XFCE, AntiX, MX, Puppy Are all good to try Puppy would run nicely on that machine. But it's non standard in many ways.

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To this I would add that the recent Void Linux-based "Kennel Linux" OSs are very much worth looking at, too.

The original Kennel Linux variant - and the most mature - KLV "Airedale" uses the XFCE/Thunar combo, and is updateable via Void's XBPS package management system. Behind the scenes, it uses several of Puppy's time-honoured "frugal" techniques.....but to the user, it's very much like many other lightweight distros that are commonly mentioned.

Be under NO illusions, though; this is NOT a 'Puppy'.......so don't try to treat it like one.

You can find the Kennel Linux section here at the Puppy Forums:-

https://forum.puppylinux.com/viewforum.php?f=192

.....and "Airedale" has its own dedicated site:-



Mike.

There are several lightweight desktops such as LXDE, LXQT, XFCE, then there are some that use a Window Manager instead of a desktop like Sparky Linux Minimal GUI, then there is Puppy Linux, Antix, and SLAX, so you have your options I would download a few and try them out on a USB stick and find the one you like