The function is

First consider the two components separately which determine the function .

The function is continuous is continuous for .

Substitute x = 2 in the above expression

The function is continuous 

is continuous for .

Substitute x = 2 in the above expression

For the limit to exist, the left hand limit and the right hand limit must be equal

 2c + 6 = 5

Subtract 6 from each side.

2c + 6 - 6 = 5 - 6

2c = - 1

Divide each side by 2.

c = -1/2.

Therefore the value of c is -1/2.