Assuming all of the fragments are drawn N-to-C, you need to look for overlaps where the last AA in one fragment is the first in another fragment.
(1) Val is first in Val-Gly-Pro and last in Ala-Val
(2) Pro is first in Pro-Ala-Gly and last in Val-Gly-Pro
(3) Gly is first in Gly-Gly and last in Pro-Ala-Gly
This means we have Val-Gly-Pro and Pro-Ala-Gly that are actually Val-Gly-Pro-Ala-Gly. It also means we have Ala-Val and Val-Gly-Pro that are actually Ala-Val-Gly-Pro.
Combining the above, we have Ala-Val-Gly-Pro and Val-Gly-Pro-Ala-Gly that are actually Ala-Val-Gly-Pro-Ala-Gly, which gives us six of the seven amino acids in the heptapeptide. There is no fragment ending in Ala, so it must be the first AA in the sequence. The only fragment to consider still is Gly-Gly, which combines with Pro-Ala-Gly to be a segment of Pro-Ala-Gly-Gly.
This leads to an overall connectivity of Ala-Val-Gly-Pro-Ala-Gly-Gly.