Non-cash means no cash payment is involved - it is something of an estimate/accrual nature
A charge is an expense - i.e. something that reduces earnings
After-tax means they have adjusted the tax estimate for the effects of this transaction i.e. the actual transaction was for an amount more or less than the $29M - the $29M is the NET amount after considering the increase or decrease in the tax expense estimate that is usually shown at the bottom of an income statement
I am not familiar with this company or transaction, but to me it sounds as though they may have bought White Mountain Cable and recorded an asset called "goodwill" (which is the excess of the purchase price over the actual market value of the net assets and liabilities purchased); subsequently, the amount of goodwill recorded was found to be too high, probably because one of the assets purchased was recorded at a value that was too low initially, or a liability was recorded at a value that was too high i.e. the net assets purchased were discovered to be worth more than recorded, and therefore the goodwill amount should have been less. The "impairment charge" is an entry booked to reduce the goodwill - it would show up as an expense type item on the income statement. There may be other reasons why goodwill may be impaired, but basically "impaired" means you have to lower the amount you are currently carrying it at on the balance sheet, and that results in a charge to income (or an expense). There will be no cash outlay - these are accounting estimates only.
Hope that helps somewhat.
