Q: how to increase the memory on the disk image in Disk Utility?

Delete the image and create a new one with more space allocated. You cannot increase the space of an extant image file.

Unless you configured the disc image as a "sparsebundle," then, no. A disk image is normally created at a fixed size you set when you make the image file.

A sparse bundle is set with a starting size and a maximum size. It can expand from the minimum size to the maximum size as usage requires. But only as much as the maximum size limit.

If you used the ordinary read/write format then you cannot enlarge it, as I stated earlier.

uvilichat

I don't know what that means.

If you wish to make a sparse bundle image, then start with:

Open Disk Utility.

Select New > Blank Disk Image from the File menu.

Put in a name for Save As field.

Set other desired criteria.

Lastly, from the Image Format dropdown menu select Sparse bundle disk image.

OK. Now you have me completely confused. Are you trying to create a Time Machine backup of your hard drive? That does not require a disk image or any image file.