Teflon tape will likely make this problem worse.
Threaded fittings for fluids basically come in two types - thread sealed, or gasket sealed.
Fittings made to be sealed by the threads have threads designed to draw themselves together as you tighten them - the fittings are slightly tapered, so as you tighten the threads, the tolerance between the threaded surfaces decreases to the point of being near-zero. The fittings slowly get harder and harder to turn until the threads are basically binding together. These fittings need a sealant to take up the last tiny amount of space and to account for manufacturing tolerances. This is what teflon tape or liquid "pipe dope" sealants are made for.
Other fittings use straight threads, similar to the threads on nuts and bolts. These threads are designed with a specific tolerance between the parts that allows them to thread fully on without any interference. Threads in this style of fitting are not designed to seal and will do a poor job, at best, of sealing the liquid passing through the fitting. Instead of the threads providing a seal, there is typically a gasket (or a flared surface acting as a gasket) inside the fitting. The threads are there to provide clamping pressure to hold that gasket snug between the mating surfaces inside the fitting. In order to do this, the threads need to be free to allow you to tighten the parts together properly. You don't want the threads to bind as they get tighter, because that could mean you're not able to actually snug the gasket down, or it could mean that you incorrectly think the gasket is snug before it is. The threads need to turn freely until the fitting is snug against the gasket. While a fitting with tapered threads will slowly get tighter as you turn it, a fitting with a gasket will spin freely until it's bottomed out against the gasket - it'll feel more like spinning a nut down a bolt until it's bottomed out.
Putting teflon tape on such a fitting is an easy way to screw it up. If you only put a small amount of tape on, it may provide enough lubrication that it makes it easy to accidentally over-tighten the fitting, which can either deform the gasket, or crack one of the two parts. If you put a lot of tape on, it will make it impossible to engage the threads deeply enough to actually clamp the gasket down between the two surfaces. Either way, the tape has created a problem. Even if you magically manage to put just enough tape on that neither of those situations occurs, using tape to seal the threads will not actually seal the fitting itself, unless the gasket is operating properly - you can see by looking at the female fitting of the elbow you have that if the gasket wasn't there, water could leak around the base of those threads and out the "top" of the fitting even if the threads were sealed. The tape hasn't actually solved the problem, even if it's not causing problems. You still need the gasket to do the sealing.
So - tape is the wrong idea here. Take the tape off, inspect both sides of the fitting to make sure there is no damage. The plastic threads on the male side are very easy to strip and you may have already stripped or cracked them in your earlier attempts. If the part is damaged, contact the manufacturer to get a replacement. Usually that plastic fitting is on a removable plate that's gasketed to the machine, so you can replace it easily.
If the parts aren't damaged, go ahead and attempt to put the fitting in place again. Make sure there's no strain introduced by the flex line on the other end of the elbow - make sure the threads are going on straight, and the fitting is tightened down to the point that the gasket is clamped in place.
If it still leaks, then you may need to contact the manufacturer for replacement parts anyways. And next time, be careful as you thread it on so as to not damage the threads, and don't use tape!
Also, find a new handyman...
