\(\mathop {{C_6}{H_{10}}}\limits_{Cyclohexene}  + {H_2} \to \mathop {{C_6}{H_{12}},}\limits_{Cyclohexane} \,\,\,\,\,\,\,\,\,\,\,\Delta {H_1} = ?.....(1)\)

Let us write the given facts

\({H_2} + \frac{1}{2}{O_2} \to {H_2}O;\)

\(\Delta {H_2} =  - 241\,\,kJ/mol.....(2)\)

\({C_6}{H_{10}} + \frac{{17}}{2}{O_2} \to 6C{O_2} + 5{H_2}O,\)

\(\Delta {H_3} =  - 3800\,kJ/mol.....(3)\)

\({C_6}{H_{12}} + 9{O_2} \to 6C{O_2} + 6{H_2}O,\)

\(\Delta {H_4} =  - 3920\,kJ/mol.....(4)\)

The required reaction \((1)\) can be obtained by adding equations \((2)\) and \((3)\), and subtracting \((4)\) from the sum of \((2)\) and \((3)\).

\({C_6}{H_{10}} + {H_2} \to {C_6}{H_{12}}\)

\(\Delta {H_1} = (\Delta {H_2} + \Delta {H_3}) - \Delta {H_4}\)

\( = [ - 241 + ( - 3800)] - ( - 3920)\)

\( = ( - 241 - 3800) - ( - 3920)\)

\( =  - 4041 + 3920 =  - 121\,kJ/mol\)