The charity Save the Children said Mohammad, which is a pseudonym, along with his wife and three children were living in eastern Afghanistan when the Taliban launched its takeover last summer.
They made it to Kabul where they spent three days outside the airport trying to secure their escape - eventually the family managed to board an evacuation flight to Ukraine, where Mohammad had previously lived and worked for 30 years.
However, as they began to settle into their new lives in eastern Ukraine, Russia launched an invasion on February 24.
As the fighting started, the family heard explosions in the distance and made the decision to leave their home once again.
Speaking to the charity Mohammad, 54, said: “My family came here for peace. But when they heard fighting would start here…nobody could believe that there would be bombing, there would be fighting. But it was real. It was not a dream.”
His 14-year-old son, Samad, also using a pseudonym, said: “It [in Afghanistan] was war and it was bombing and very bad days. A lot of people were killed in this war. So we left Afghanistan."
Samad said moving to Ukraine had been a good thing for his family, adding he had made friends and been to school, but he said the situation there had become just like Kabul.
"A lot of people wanted to leave and go to a peaceful place, for their children, for themselves.
“In the future I will miss a lot of things that I had there. [But] for us it’s a very big thing for us to be safe, it’s enough for us to be safe here.”
The family drove for more than 30 hours on crowded roads before waiting three days at the border, sleeping in their car while temperatures plummeted outside.
They eventually managed to cross the border and are currently in Suceava, Romania.
The family are now being supported by Save the Children, which is working in the reception centre where they are currently staying, and has provided them with information and guidance, clothes and shoes.
The aid agency, which is a member of the Disaster Emergency Committee (DEC), is also on the border distributing food, blankets and hygiene kits.
Samad said: “We’re just in a camp, and I’m worried for my future. I want to study, I want to be a good man. For my family, for my future, for myself.”
"Everything will be right. I think so. I hope so", Mohammad added.
Donations raised by the DEC’s Ukraine Humanitarian Appeal are being used to help people like Samad and his family to help rebuild their lives.
More than £150 million has been raised since the DEC launched its appeal last week, which includes £25 million matched by the UK Government.
Gabriela Alexandrescu, chief executive of Save the Children Romania, said: “Children and families across Ukraine are facing impossible decisions every day. The choice between retreating below ground to try and survive a terrifying onslaught or abandoning everything and escaping as conflict rages is one no parent should have to make.
“To be forced to flee across borders twice in the space of months is almost impossible to conceive.
“Many people originally from outside Europe are fleeing Ukraine and they need Europe’s help and protection.”