From the 4th to the 8th of June - [date ranges]

In a business letter, what's the correct or more frequent way to write date ranges?

from the 4th to the 8th of June 2014, we have been working on the project

or

from 4 to 8 June 2014, we have been working on the project

or

In June 2014, 4 to 8, we have been working on the project

Both forms are acceptable. The use of 8th is more common than either 8 June or the eighth of June.

Because both dates are in the past, consider using past tense.

"We worked on the project from June 4th 2004 through June 8th 2014."

The use of through is slightly less ambiguous.

From June 4th through 8th of 2014...

or

From the 4th through 8th of June in 2014...

or

From June 4 through June 8, 2014

The first option you posted is normal, but the other two are nonstandard.