Function Equality and Constant Determination

Let the function $$ f $$ be defined as follows:

$$ f(x) = 4x - 3 $$

Let another function $$ g $$ be defined as:

$$ g(x) = x^2 + k $$

where $$ k $$ is a constant. If it is known that $$ f(g(2)) = g(f(2)) $$, determine the value of the constant $$ k $$.