Let's denote the man's speed for the first 4 km as \(v\) km/h. Then his speed for the rest of the distance (5 km) is \(v + 2\) km/h.

The total time he spends running is 1 hour, which is the sum of the time he spends running the first 4 km and the time he spends running the last 5 km. This can be expressed as:

\(\frac{4}{v} + \frac{5}{v + 2} = 1\)

We can solve this equation for \(v\) to find his average speed for the first 4 km.

Multiplying through by \(v(v + 2)\) to clear the fractions gives:

\(4(v + 2) + 5v = v^2 + 2v\)

Simplifying gives:

\(v^2 - 7v - 8 = 0\)

This factors to:

(v - 8)(v + 1) = 0

The solutions are v = 8 and v = -1. 

Since speed cannot be negative, we discard v = -1 and are left with v = 8km/h.

So, his average speed for the first 4 km is 8 km/h.