Hi,
I just installed Linux Elementary alongside with Win 10. While doing that, I created 3 partitions:
1) /root -10GB
2) swap-8GB
3) /home -30 GB

The problem is, my OS is on /root which is just 10gb and I can't access those 30gb. Here are the pictures of partitions:
In the first picture, the last 3 partitions are Linux, and in the second picture the File System shows only 10GB instead of 30GB. IS there any way to fix this?

Attached Thumbnails

   

There's nothing to fix. The 30GB partition is available under /home and should be available for you to store data. 8GB is pretty small for a filesystem partition and 8GB is large for swap.

I can't access the /home. /home is under /root, which is 10gb. Or I don't know how to. 8gb for swap is not too much.

When I try to install program I can only choose this one, 10gb, not 30

Can you please paste the output from the following command:

# /etc/fstab: static file system information.
#
# Use 'blkid' to print the universally unique identifier for a
# device; this may be used with UUID= as a more robust way to name devices
# that works even if disks are added and removed. See fstab(5).
#
# <file system> <mount point> <type> <options> <dump> <pass>
# / was on /dev/sda5 during installation
UUID=0a265f8b-3bc3-42bf-a533-d08eaacf71f7 / ext4 errors=remount-ro 0 1
# /boot/efi was on /dev/sda2 during installation
UUID=020C-2C2D /boot/efi vfat umask=0077 0 1
# /home was on /dev/sda7 during installation
UUID=e16e4868-8f9e-4a6a-9ebf-da5c5f844331 /home ext4 defaults 0 2
# swap was on /dev/sda6 during installation
UUID=c7c9ded6-3732-4049-958d-4a67cde76a7e none swap sw 0 0

That looks fine to me. Any files that you place in /home or its subdirectories will be on that 30GB partition.

It doesn't come up as an extra Device in your file manager because it isn't viewed as one - when mounted in /home, it is an integral part of your root filesystem.

But why it says like this? Does this mean something?

Attached Thumbnails

 

Ok. Let's check. Can you paste the output from:

Filesystem 1K-blocks Used Available Use% Mounted on
udev 3940808 0 3940808 0% /dev
tmpfs 794516 1688 792828 1% /run
/dev/sda5 9777660 5697696 3563564 62% /
tmpfs 3972572 10460 3962112 1% /dev/shm
tmpfs 5120 4 5116 1% /run/lock
tmpfs 3972572 0 3972572 0% /sys/fs/cgroup
/dev/sda2 98304 31424 66880 32% /boot/efi
/dev/sda7 33624744 2828348 29058620 9% /home
tmpfs 794512 100 794412 1% /run/user/1000
/dev/sda4 447047676 155851084 291196592 35% /media/alma/2E360E1A360DE3A5

That looks good. You should trust df rather than your file manager. I have to say though that 10GB for the non /home section of a Linux distro's filesystem is probably too small. You will most likely have to look at increasing that. I always give my root filesystem 20GB for example. However, that's a separate issue that will have to be addressed.

Which file manager are you using? Can you paste a complete screenshot of that left sidebar?

The default one, "Files".

Attached Thumbnails

 

Ok, thanks. Your file manager has probably decided that it's not going to show you /dev/sda7 as a separate device because you can get to that device just by clicking on the Home link at the top (which is close enough as that will give you /home/alma or similar, depending on your username - you won't have much else, if anything, in /home). Let me know if that doesn't make sense.

This is perhaps configurable in your file manager.

The upshot is that you're good to go and that you're just going to have to use df or another means to determine how much space you have left in /home as this info doesn't appear to be available in Files. You could always try right-clicking on Home at the top and see if there is a context menu with, say, a Properties option.

But when I try to install program, I can only choose this one, Not the 30gb

Attached Thumbnails

 

That's where programs get installed by default, in the main root filesystem. Your home directory structure is mostly for documents, videos, photos, other data files, and personal configuration files. That's why you probably don't have enough space in your root filesystem with only 10GB.