If \[{{\mathbf{4}}^{\mathbf{x}}}\mathbf{ = }{{\mathbf{2}}^{\mathbf{y}}}\mathbf{ = 1}{{\mathbf{6}}^{\mathbf{z}}}\mathbf{= 256}\], then find the value of \[{{\mathbf{x}}^{\mathbf{2}}}+\text{ }{{\mathbf{y}}^{\mathbf{2}}}+\text{ }{{\mathbf{z}}^{\mathbf{2}}}+\text{ }\mathbf{2xy}\text{ }+\text{ }\mathbf{2yz}\text{ }+\text{ }\mathbf{2zx}.\]

• A. 120 
• B.  196
• C.  186     
• D.  190
• E.  None of these