From what I see you have a system partition and a Windows partition followed by a small 4Gb partition and a Windows recovery partition.
To get Ubuntu on this machine you will need to remove one partition, replace it with an extended partition. Then, in the extended partition, you may create your Ubuntu (mount point /) and swap partitions.
I have never done this but one possible solution is to use an Ubuntu live CD or live USB, to:
- Do a backup of one of the partitions, say the small 4Gb one with
dd -if /dev/sda3 > partitionimage.dd. Modify thr path of the partitionimage.dd file to an external disk (ex.
- Delete that partition.
- Reduce the Windows partition by say 30Gb.
- Create an extended partition in the empty space left by the two partitions.
- Create your two Ubuntu partitions in the extended partition and another 4Gb one.
- Restore the backup of your original 4Gb partition in this new partition by navigating in a terminal to the folder where the backup file is and type
dd -if partitionimage.dd -of /dev/sda3. Change /dev/sda3 with your new reference for the new partition (ex. /dev/sda6)
WARNING: I never did the backup and restore bit of this procedure so I would wait for someone to review it before going through it.
WARNING 2: This is a MAJOR OPERATION and if something went wrong you could loose everything. Be sure to have a Windows recovery disk and an external backup of your data just in case.