A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is:

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1. **Let the speed of the train be $$ x $$ km/hr and the time taken be $$ T $$ hours:**  
   - Distance travelled = $$ x 	imes T $$.

2. **Case 1 (Speed increased by 6 km/hr):**  
   - New speed = $$ x + 6 $$ km/hr.  
   - Time taken = $$ T - 4 $$ hours.  
   - Distance remains the same:  
     $$
     xT = (x + 6)(T - 4)
     $$  
     Expand and simplify:  
     $$
     xT = xT + 6T - 4x - 24
     $$  
     $$
     6T - 4x = 24 \quad 	ext{(Equation 1)}
     $$

3. **Case 2 (Speed decreased by 6 km/hr):**  
   - New speed = $$ x - 6 $$ km/hr.  
   - Time taken = $$ T + 6 $$ hours.  
   - Distance remains the same:  
     $$
     xT = (x - 6)(T + 6)
     $$  
     Expand and simplify:  
     $$
     xT = xT - 6T + 6x - 36
     $$  
     $$
     -6T + 6x = 36 \quad 	ext{(Equation 2)}
     $$

4. **Solve the equations:**  
   From Equation (1):  
   $$
   T = \frac{4x + 24}{6}
   $$  
   Substitute into Equation (2):  
   $$
   -6\left(\frac{4x + 24}{6}ight) + 6x = 36
   $$  
   Simplify:  
   $$
   -(4x + 24) + 6x = 36
   $$  
   $$
   2x = 60 \implies x = 30
   $$

5. **Find time ($$ T $$):**  
   Substitute $$ x = 30 $$ into Equation (1):  
   $$
   T = \frac{4(30) + 24}{6} = \frac{120 + 24}{6} = \frac{144}{6} = 24
   $$

6. **Calculate distance:**  
   Distance travelled = $$ x 	imes T = 30 	imes 24 = 720 \, 	ext{km} $$.

Thus, the distance travelled by the train is **720 km**.

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