assuming times are entered in proper time format (like 6:35 AM or 5:45 PM) in column A and reasons in B, formula in C2 (copied down)
=IF(OR(B2="Clearing & Stacking Timber",B2="Other Chargeable Reason"),A3-A2,0)
or
=IF(AND(B2<>"Prestart Machine",B2<>"Crib",B2<>"Service Machine"),A3-A2,0)
if the number of reasons not chargeable is more than the chargeable, i recommend you use formula 1.
other methods can be found as well.
you can calculate the time not chargeable in column D like:
=IF(OR(B2="Prestart Machine",B2="Crib",B2="Service Machine"),A3-A2,0)