Most restriction enzymes have a 6bp restriction site (some have 8bp site also). So two restriction sites generally have to span 12bp. However some restriction sites can overlap. For example BamHI and SmaI:
In this case the total length has reduced to 10bp. However such combinations are not that common and at max you will achieve a 2-3bp overlap. A restriction endonuclease only makes a single cut. To make double cuts you need two restriction sites.
Even if the sites are non-overlapping there has to be a minimum length of separation otherwise the binding of one enzyme will hinder the binding of the other enzyme in a double digest. A 6 nucleotide gap between the restriction sites should be fine. If there is no gap then double digest may not be very efficient.
You can also have two restriction sites of the same enzyme so that you need not use two separate enzymes.
BTW the sequence in your question does not have any restriction site.
Hope this answers your question.