Assertion:- First law of thermodynamics doesn’t forbid flow of heat from lower temperature to higher
temperature
Reason:- Heat supplied to a system always equal to the increases in its internal energy

1^st is correct,2nd is wrong because heat supplied is proportional toincrease in internal energy.2nd is correct explanation of first.

First law of thermodynamics is basically explains energy conservation in a thermodynamic system. Therefore it does allow flow of heat from cold reservoir to hot reservoir. Now, the second law of thermodynamics was introduced to ensure that nothing logically unsatisfying statement like the one above prevailed in physics.

The reasoning behind the given assertion has nothing to do with heat supplied and increase/decrease in internal energy. In fact, heat supplied to a thermodynamic system is only absorbed by the working substance (gas molecules) to increase internal energy when the process is perfectly ideal and isochoric.